In particular: the telepathy spell (PHB, p. 281) states:
[...] The creature can be anywhere on the same plane of existence as you. The spell ends if you or the target are no longer on the same plane. [...]
Can telepathy connect two characters, one inside the extradimensional dwelling created by the Mordenkainen's magnificient mansion spell and the other in the same plane as the portal to the magnificent mansion?
The Dungeon Masters Guide (DMG) has this to say on Demiplanes:
Demiplanes are extradimensional spaces that come into being by a variety of means and boast their own physical laws. Some are created by spells. Others exist naturally, as folds of reality pinched off from the rest of the multiverse. Theoretically, a plane shift spell can carry travelers to a demiplane, but the proper frequency required for the tuning fork would be extremely hard to acquire. The gate spell is more reliable, assuming the caster knows of the demiplane.
A demiplane can be as small as a single chamber or large enough to contain an entire realm. For example, a Mordenkainen’s magnificent mansion spell creates a demiplane consisting of a foyer with multiple adjoining rooms, while the land of Barovia (in the Ravenloft setting) exists entirely within a demiplane under the sway of its vampire lord, Strahd von Zarovich. When a demiplane is connected to the Material Plane or some other plane, entering it can be as simple as stepping through a portal or passing through a wall of mist.
From this we can see that the space created by Mordenkainen's Magnificent Mansion (MMM) is a Demiplane.
The Telepathy spell has this text:
The creature can be anywhere on the same plane of existence as you. The spell ends if you or the target are no longer on the same plane.
From the DMG rules on demiplanes it is clear that the MMM demiplane is not the same plane of existence as the plane where the entrance to MMM was created from. This is made explicit by the fact that the Plane Shift spell requires a tuning fork tuned to the demiplane specifically to access them.
We can see this from Plane Shift's material component:
a forked, metal rod worth at least 250 gp, attuned to a particular plane of existence
As a result Telepathy will not work between outside MMM and inside MMM.
While there are no official rulings regarding Extradimensional and planes of existence in the Curse of Strahd Alterations to magic. (Placing it in spoiler as to not to spoil the game for people).
Magic that summons creatures or objects from other planes functions normally in Barovia, as does magic that involves an extradimensional space. Any spells cast within such an extradimensional space (such as that created by Mordenkainen's Magnificent Mansion) are subject to the same restrictions as magic cast in Barovia.
--Curse of Strahd P24 Alterations to Magic
From the fact that this is an alteration to the existing rules we can deduce that according to the original rule spells that are cast in the extradimensional spaces are not bound to the plane of existence the space originates from.
Considering that each plane has it's own traits and extradimensional space is seperate from the said traits we can say that extradimensional spaces are not part of the plane they originate from thus disallowing spells and abilities that require being in the same plane such as telepathy.
The background on demiplanes found in the DMG conflicts with the rules outlined in Curse of Strahd. The DMG is more vague and descriptive, being meant to cover every possible kind of demiplane. Curse of Strahd is much more specific in describing the interactions of two particular demiplanes (Barovia and a magnificent mansion). Because CoS is written as specific rules text while the DMG is written as general background campaign description, I center my understanding of how the mansion works on the passage in CoS. In the introductory section on Alterations to Magic, we can read:
The land of Barovia resides in its own demiplane, isolated from all other planes, including the Material Plane. No spell—not even wish—allows one to escape from Strahd's domain. Astral projection, teleport, plane shift, and similar spells cast for the purpose of leaving Barovia simply fail, as do effects that banish a creature to another plane of existence. These restrictions apply to magic items and artifacts that have properties that transport or banish creatures to other planes.
One cannot leave Barovia by spells - full stop. It functions as its own plane (although not truly one), and magic will not permit one to leave Barovia and enter another plane. If this was all that CoS told us, and if we believed that Magnificent Mansions existed on planes other than the ones they were cast on, that is, if the door of a mansion functioned as a planar portal, we would have to conclude that any attempt to cast MM in Barovia would simply result in the spell failing, as astral projection and plane shift do, and as teleport would do if the destination chosen were outside Barovia.
However, CoS does not stop there. Later in the same section it says,
For the purpose of spells whose effects change across or are blocked by planar boundaries (such as sending), Strahd's domain is considered its own plane. Magic that summons creatures or objects from other planes functions normally in Barovia, as does magic that involves an extradimensional space. Any spells cast within such an extradimensional space (such as that created by Mordenkainen's magnificent mansion) are subject to the same restrictions as magic cast in Barovia.
Even though one may not leave Barovia, magic that involves an extradimensional space functions normally, including explicitly that of the mansion. If the mansion was in a different plane, one could not leave Barovia to enter it. Ergo, the extradimensional space within the mansion must also be within Barovia. Because it is actually part of Barovia, the Barovian restrictions on magic apply - including that one my not leave the space to go to a different plane. Which makes sense - if all that was required to escape the Domains of Dread was casting a magic mansion, stepping inside it to what was another plane, and then casting plane shift or teleport circle, then Strahd (or surely Vecna) would have escaped long ago.
The DMG description of these things is vague, but we know that the magnificent mansion is both an extradimensional space and a demiplane. Now that we know it is also part of the plane it is on, and not a separate plane, we can begin to understand what is meant by the other terms.
Extradimensional spaces are spaces that go beyond our normal experience of spatial dimensions - often, but not always, they are things that are 'bigger on the inside'. One can conceive of them as warped spacetime, such that the interior dimensions of an area are greater than its external dimensions. Or as Darth Pseudonym has said, extradimensional spaces are not other planes, they are "just real-space, folded weirdly."
The root demi- means "one that partly belongs to". In this sense, a demiplane is one type of plane - specifically one that is not so big and so permanent that it is mapped on the planar cosmology. Another meaning of demi- is "half", or "lesser". Given what we know about demiplanes from Curse of Strahd we can consider at least some demiplanes (e.g., mansions) to be like a sub-plane - a specific region of another plane, sometimes with some of its own physical laws, but not (necessarily) a plane unto itself. On the other hand, other demiplanes (e.g. Barovia and other Domains of Dread) may be large and effectively independent of the planes they are on (in this case, the Shadowfell).
So let's see how well these interpretations stand up to what I claimed was a vague DMG (68) definition:
Demiplanes are extradimensional spaces that come into being by a variety of means and boast their own physical laws. Some are created by spells. Others exist naturally, as folds of reality pinched off from the rest of the multiverse.
Nothing in here contradicts an interpretation that says that demiplanes are special regions of other planes but not planes in their own right.
Theoretically, a plane shift spell can carry travelers to a demiplane, but the proper frequency required for the tuning fork would be extremely hard to acquire. The gate spell is more reliable, assuming the caster knows of the demiplane.
The gate spell says "You conjure a portal linking an unoccupied space you can see within range to a precise location on a different plane of existence." In this case, the 'precise location' is the specific demiplane on the chosen different plane of existence. This implies that one could not, for example, open a gate from within a magnificent mansion to the greater plane of which the demiplane was a part, or vice versa. (If the mansion was truly a different plane unto itself, one could gate from within to the space outside its door)
The plane shift spell has as its material component "a forked, metal rod worth at least 250 gp, attuned to a particular plane of existence". This, combined with the statement in the DMG that plane-shifting to a demiplane is possible but would require a very specific tuning fork, is difficult to reconcile with the interpretation that the demiplane of the mansion is an extradimensional extension of, but still part of, the plane it was cast from. If you insist on taking this section of the DMG at face value, then the fact that you can plane shift to a demiplane implies that it is a plane in its own right and the material in Curse of Strahd does not make any sense. If you wish to retain the understanding developed in CoS, however, you need to be a bit looser in your interpretation of the DMG. Perhaps it is possible to plane shift to some demiplanes - the large and permanent ones like Barovia - but not to others - the small and temporary ones like a specific mansion. Or perhaps attempting to plane shift to a specific mansion requires a tuning fork resonating with the true plane that the mansion is on, but only lands you somewhere near the entrance door, similar to the description given in the plane shift spell: "...you appear in or near that destination. If you are trying to reach the City of Brass, for example, you might arrive in its Street of Steel, before its Gate of Ashes, or looking at the city from across the Sea of Fire, at the GM's discretion."
The DMG (68) continues:
A demiplane can be as small as a single chamber or large enough to contain an entire realm. For example, a Mordenkainen's magnificent mansion spell creates a demiplane consisting of a foyer with multiple adjoining rooms, while the land of Barovia (in the Ravenloft setting) exists entirely within a demiplane under the sway of its vampire lord, Strahd von Zarovich. When a demiplane is connected to the Material Plane or some other plane, entering it can be as simple as stepping through a portal or passing through a wall of mist.
Here, we could interpret 'connected to' to mean joined through a portal or, using the CoS example, it could mean that the demiplane was on the true plane, as a specific subregion.
For me, a further benefit of interpreting extradimensional spaces and at least some demiplanes as actually being part of their 'host' plane is that it better explains and makes some distinctions between certain spells. Some spells (rope trick, magnificent mansion, maze), can only be accessed from a certain point on a specific plane, and at the end of their duration expel anything inside them. This would make sense if these spells created infoldings of reality that pushed things out as they shrank when the spell expired - the extradimensional space and demiplane that the spell had created simply ceased to exist as the plane resumed its normal size. Other spells (demiplane, possibly the hedged prison of imprisonment) create permanent planes with temporary gateways. At the end of the spell the portal disappears but not necessarily the space, and anything still inside could be trapped rather than pushed out. These spaces can be accessed again from anywhere if recast, not just from the plane they were originally cast from. This makes sense if they are actually planes unto themselves and are not extensions of another plane.
These same distinctions also clarify magic items. A bag of holding and a handy haversack expel their contents if turned inside out, and potentially can be pierced from within, both of which make sense if they are simply extradimensional objects, larger inside than out. A portable hole, on the other hand, cannot be turned inside out or pierced from within, and it is the only such item to specifically state that its contents are on their own plane. The cloth of the hole functions as a portal to another place, not a container for an extradimensional infolding of this place.
If your mansion was cast in Barovia, the inside of the mansion is on the same plane as the outside, because if it weren't, no one could enter the mansion in the first place. Telepathy will function from inside to outside and vice versa. If you take the description in CoS to apply to all mansions everywhere, then telepathy will also work in this way anywhere. However, if you read the DMG section on demiplanes and plane shift to apply to all demiplanes everywhere, then outside of Barovia the interior of a mansion is a different plane than its exterior, and telepathy could not pass between them.
