CI: Add normal testing for Python 3.12

[lithomas1]

• 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.

[alimcmaster1]

Ref: #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.

[lithomas1]

Sorry for the lack of updates. Closing in favor of #56174.