CI: Add normal testing for Python 3.12
- [ ] closes #xxxx (Replace xxxx with the GitHub issue number)
- [ ] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [ ] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [ ] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) 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.

Ref: https://github.com/pandas-dev/pandas/issues/53665

Thanks for doing this @lithomas1 - shout if you want any help.

```
DeprecationWarning: Bitwise inversion '~' on bool is deprecated. This returns the bitwise inversion of the underlying int object and is usually not what you expect from negating a bool. Use the 'not' operator for boolean negation or ~int(x) if you really want the bitwise inversion of the underlying int.
```
^ Saw this in a few places in the test failures.
 Sorry for the lack of updates. Closing in favor of #56174.