AFAICT mouseDown() and friends already check [event type] and
correctly handle right/middle button events, so the other event handlers
can just defer to them.

The point of the deduplication is so that future event rearchitecting
(subsequent to #16931 and fixing #6159)
doesn't have to repeat loads of keyboard-modifiers handling code in each
of these handlers.

I don't actually have a mac to test this :-) so it would be nice if
someone could check if e.g. interactive zoom-out (by drawing a rubberband
with a right click) still works fine.

PR Summary

PR Checklist

• Has pytest style unit tests (and pytest passes).
• Is Flake 8 compliant (run flake8 on changed files to check).
• New features are documented, with examples if plot related.
• Documentation is sphinx and numpydoc compliant (the docs should build without error).
• Conforms to Matplotlib style conventions (install flake8-docstrings and run flake8 --docstring-convention=all).
• 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).