Alternative implementation of #10659, which addresses the issues raised in the comments.

Previously, pickling and unpickling shared axes would result in
axes sharing a ticker instance (because that's how shared axes
are set up), but without changes of one's xlims propagated to the
other. The reason is that that sharedness information is stored in
AxesBase._shared_x_axes, which does not get pickled together with the
Axes instance: the latter only has a textual reference "I am an instance
of AxesBase", so the Grouper information is lost.

this is the part of the implementation that changed

To keep the Grouper information valid, additionally pickle the current
group of shared axes together with the Axes, and restore that
information upon unpickling.

end of diff

PR Summary

PR Checklist

• Has Pytest style unit tests
• Code is PEP 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