GH-43809: [Docs] Update extension type examples to not use UUID

[khwilson]

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: [Docs] Update extension type examples to not use UUID #43809

[khwilson]

@ianmcook, apologies again for accidentally pushing my wonky branch.

The two remaining issues with the build were (1) some spacing issues arising from my IDE's formatter and copy/pasting outputs from terminals; and (b) Numpy changed the repr for float16's in 2.x so the half-float test in types.pxi was sometimes failing depending on which version of numpy was installed. I have modified this test so that it works both with numpy 1.x and 2.x.

[jonkeane]

@github-actions crossbow submit preview-docs

[github-actions]

Revision: ff67035

Submitted crossbow builds: ursacomputing/crossbow @ actions-51ff65abfb

Task	Status
preview-docs

[ianmcook]

Links to rendered previews of the relevant sections

• http://crossbow.voltrondata.com/pr_docs/44120/format/Columnar.html#extension-types
• http://crossbow.voltrondata.com/pr_docs/44120/format/Integration.html#json-test-data-format
• http://crossbow.voltrondata.com/pr_docs/44120/python/extending_types.html#defining-extension-types-user-defined-types
• http://crossbow.voltrondata.com/pr_docs/44120/python/generated/pyarrow.ExtensionType.html
• http://crossbow.voltrondata.com/pr_docs/44120/python/generated/pyarrow.register_extension_type.html
• http://crossbow.voltrondata.com/pr_docs/44120/python/generated/pyarrow.unregister_extension_type.html

[ianmcook]

Thanks @khwilson! This looks great. I will merge this soon unless @rok, @jorisvandenbossche, or others have any further comments.

[ianmcook]

@github-actions crossbow submit preview-docs

[github-actions]

Revision: 0502ff8

Submitted crossbow builds: ursacomputing/crossbow @ actions-8955adf366

Task	Status
preview-docs

[ianmcook]

Thanks again @khwilson!

[conbench-apache-arrow]

After merging your PR, Conbench analyzed the 4 benchmarking runs that have been run so far on merge-commit 0d4badb.

There were no benchmark performance regressions. 🎉

The full Conbench report has more details. It also includes information about 4 possible false positives for unstable benchmarks that are known to sometimes produce them.