Simplify qt_compat, in particular post-removal of qt4 support.

[anntzer]

Also note that None is never keyed off _ETS, which allows removing
the None: None entry have some more simplifications.
Also avoid the need for exception chaining suppression (raise ... from None).
Also clarify the error message when no qt binding can be imported
(the original motivation here; see #22673 (comment)).

PR Summary

PR Checklist

Tests and Styling

• Has pytest style unit tests (and pytest passes).
• Is Flake 8 compliant (install flake8-docstrings and run flake8 --docstring-convention=all).

Documentation

• New features are documented, with examples if plot related.
• New features have an entry in doc/users/next_whats_new/ (follow instructions in README.rst there).
• API changes documented in doc/api/next_api_changes/ (follow instructions in README.rst there).
• Documentation is sphinx and numpydoc compliant (the docs should build without error).