I am trying to write something similar to $\frac{a}{b} more words$ but using over (manim requires that it must be with over) but when writing $a\over b more words$ the "more words" appear in the denominator.
How can this issue be solved?
Well the solution is simply using { } brackets like so: {a \over b} some words
\over you should always write {{a} \over {b}}.
\frac macro adds \begingroup and \endgroup around the first argument, because local assignments in it might spill to the denominator.
$a\let\x\relax\over b\show\x$. Without the grouping, something like \frac{\bf a}{b} would have both letters in boldface. Now \bf is deprecated, I know, but that's the rationale for adding the group.
{{a}\over{b}} seems dubious.
\fracnot\over: why must you use the latter?