I spent some time yesterday and today trying to get tests to run on old versions of Matplotlib which....was harder than I wished it would be. We may want to have one very pinned requirements file (possible managed by one of the auto-bump services 😞 or tools) that we rename to fully-pinned-v3.6.x.txt on branching. We can then use that (exclusively) for tests on the backport branch which should hopefully reduce the amount of dep-only backports we have to do (and provide a useful reference for anyone who wants to get old versions testing again).

Originally posted by @tacaswell in #22574 (comment)