Most importantly, the current backend is mostly irrelevant (unlike what
the docs state), because we handle backend switching transparently.

Preliminary work for #13253 (comment).

Note that the actual behavior is actually slightly different from the documented one: if the active canvas is PDF, PS or SVG and a format cannot be derived from fname or from format, then the format used will be pdf/ps/svg (respectively) rather than rcParams["savefig.format"]. I would like to change that to instead always use the rcParam, but that'll wait for #12760 first (for rebase reasons). (Why allow saving to png when using a pdf canvas? Because to me that's similar as allowing to save to pdf when using an agg (=raster) canvas, and transparently handling the backend switching.)

PR Summary

PR Checklist

• Has Pytest style unit tests
• Code is Flake 8 compliant
• New features are documented, with examples if plot related
• Documentation is sphinx and numpydoc compliant
• Added an entry to doc/users/next_whats_new/ if major new feature (follow instructions in README.rst there)
• Documented in doc/api/api_changes.rst if API changed in a backward-incompatible way