DOC: Run all doctests

[rhshadrach]

• closes #xxxx (Replace xxxx with the GitHub issue number)
• Tests added and passed if fixing a bug or adding a new feature
• All code checks passed.
• Added type annotations to new arguments/methods/functions.
• Added an entry in the latest doc/source/whatsnew/vX.X.X.rst file if fixing a bug or adding a new feature.

It appears that if the __module__ value of the class does not agree with the __module__ value of the methods, then the doctests do not run.

Still verifying if this is correct and investigating the best way to handle it.

Edit: Indeed, CI is showing many wrong docstrings due to this.

There are two approaches I am considering here:

1. Use an env variable similar to what this PR is currently doing to not set the __module__ values when we run the doctests. The downside is that we'd need to not have the __module__ value appear in any of the example's output because e.g. pandas.Series would appear as pandas.core.series.Series.
2. Set the __module__ on all class methods via the set_module decorator using inspect (automatically iterating through class methods and modifying the __module__ attribute). This would increase import time (not sure by how much) and it wouldn't work on cdef classes.

[jbrockmendel]

Yikes. I like the env variable approach more than then set_module-on-all-classmethods approach. Is there a "hope for a fix upstream" option?