This is in preparation for#27663, moving the various hardcoded backend lists and dicts to a newBackendRegistry class that is intended to be the single source of truth for backends. There is no functional change.

There is a singletonbackend_registry instance of theBackendRegistry class inregistry.py. This is a similar implementation to that of the singletonrcParams instance of theRcParams class.

BackendRegistry includes the two public functions that are currently needed. There will eventually be alist_all function to list all backends including the built-in ones, those obtained via the"module://blah.blah" approach, and those registering themselves via entry points. The class internals will change too of course.

There are still some hardcoded backend names in_fix_ipython_backend2gui, but this will be addressed as part of the wider#27663 implementation.

I have not yet added an API change note. Thebackend_registry could be considered internal to Matplotlib except that IPython will also use it, so it could be thought of as fully public, or private with an exception for IPython. Other use of built-in backend lists by downstream libraries is probably restricted to use ofrcsetup.interactive_bk,non_interactive_bk andall_backends. I have deprecated them in this PR to demonstrate that this is convoluted as they are module-level attributes that need to be deprecated using the recommendations of PEP 562. But probably I would be more inclined to keep them for the moment, until we are sure how this will all work in the end, and just pass through thebackend_registry results.

(Edited to change name of singleton instance)