Convert matplotlib to bidirectional communication plugin

As a user of matplotlib, I would like it to have a richer experience. Right now it's built on top of input tables, and kind of janky. Now that we have bidirectional communication, we should be able to rip that part out.
Ideally we should leverage the WebAgg frontend for enhanced matplotlib experience: https://matplotlib.org/stable/gallery/user_interfaces/embedding_webagg_sgskip.html