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Most methods to create an Axes instance (e.g. Figure.add_axes, pyplot.subplot) allow passing of the projection keyword in order to return an instance of a subclass of Axes. It would be useful if Axes.inset_axes could do the same.
See also #22608 where there was some agreement that this would be useful, but that was not the right solution.
Proposed solution
I'm unfamilar with the Matplotlib codebase, but I think the relevant functionality is contained within Figure._process_projection_requirements. So perhaps inset_axes could reuse that somehow.