Add debug option to check category MRO

[user202729]

To avoid headaches like #39154 in the future.

TODO: set this option to False by default.

TODO: make the test actually pass for homset. As the documentation says "currently this doesn't work with homset"…

📝 Checklist

• The title is concise and informative.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation and checked the documentation preview.

⌛ Dependencies

• Add _make_named_class_key for several categories, miscellaneous changes #39160 : Not strictly necessary, but to avoid the newly-found failures .
• Return True instead of None to avoid cachefunc being useless #39174 : same as above. (also need to split this into separate PR for cachefunc debug feature)

[github-actions]

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[user202729]

The caching really breaks a lot of things.

sage: MatrixSpace(SR, 2).category()
Category of infinite finite dimensional algebras with basis over commutative rings
sage: SR.category()
Category of commutative rings
sage: VectorSpaces(SR)
Category of vector spaces over Symbolic Ring
sage: SR.category()
Category of fields
sage: MatrixSpace(SR, 2).category()  # cached!
Category of infinite finite dimensional algebras with basis over commutative rings
sage: MatrixSpace(SR, 3).category()
Category of infinite finite dimensional algebras with basis over fields

Of course with the band aid this particular one is fixed but…

Might be a better idea to use the category with axiom framework, whatever it may mean.