arrow

GH-43809: [Docs] Update extension type examples to not use UUID (#44120)

### Rationale for this change

UUID extension types were made canonical in #41299 and are getting
native support in C++ and Python in #37298. As such, it makes sense to
provide an alternative user-defined extension type as an example that is
unlikely to become a canonical extension type anytime soon.

After discussion in #43809, we determined a `RationalType` would make
sense.

Please note that this is a redo of #43849 as I made a blunder and
accidentally pushed a branch that was in a wonky state.

### What changes are included in this PR?

A change in several doc locations which reference a `UuidType` extension
type have been changed to a `RationalType`.

For consistency, this PR also changes single quotes (`''`) to double
quotes (`""`) throughout the Python examples that it modifies.

Also, seemingly unrelated to this change, some doctests began failing as
numpy changed the `repr` of `float16`'s between 1.x and 2.x. We have
updated the failing doctest so that it supports both styles.

### Are these changes tested?

These are documentation changes and `archery docker run
conda-python-docs` succeeds locally.

### Are there any user-facing changes?

No.

cc @ianmcook @rok 
* GitHub Issue: #43809

---------

Co-authored-by: Ian Cook <ianmcook@gmail.com>