Fix pickling of axes property cycle. #26341
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Instead of relying on itertools.cycle (which is unpicklable, and leads to the axes property cycle being reset to the rcparams value upon unpickling), use a plain, trivially picklable, list-and-index representation (the property cycle is guaranteed to be finite because Axes.set_prop_cycle passes its argument through matplotlib.cycler, which already iterates through all cycler values for validation purposes).
Unfortunately this is not enough to really get rid of the get_next_color/get_next_color_func awkwardness, which also serves the additional purpose of not unnecessarily advancing the prop_cycle when it does not contain a "color" key and a color is requested.
Closes #26082.
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