Since the Genie's Vessel is described as an object/vessel and never as an item, is it safe to bring a Portable Hole, Bag of Holding, or Heward's Handy Haversack into the bottle?
If your vessel is a ring per the examples, is it splitting hairs to not call it an item?

Genie's Vessel: -- Tashas p.73
The vessel is a Tiny object, and you can use it as a spellcasting focus for your warlock spells.

Bottled Respite: -- Tashas p.74
The interior of the vessel is an extradimensional space in the shape of a 20-foot-radius cylinder, 20 feet high, and resembles your vessel.

Bag of Holding: -- DMG p.154
Placing a bag of holding inside an extradimensional space created by a Heward's handy haversack, portable hole, or similar item instantly destroys both items and opens a gate to the Astral Plane.