Current status:

• We vendor our own sphinx theme that is based on an ancient verson of the alabaster theme. which has been heavily modified over time. The theme is a bit hard to maintain, and things can fall apart if sphinx does some changes (indeed we recently had a broken search Fix sphinx search #19279).
• The current layout is not responsive.
• Parts of the current layout look dated (which is subjective of course).

Proposal:

Reuse https://github.com/pydata/pydata-sphinx-theme, which has been adopted by some major numfocus projects.

I anticipate less maintainance effort on our side, because the theme is shared between multiple major projects.

I like the idea that major numfocus projects have similar but still distinct designs. One should recognize that numpy and matplotlib are related, but I still want to immediately see if I'm on numpy, pandas or matplotlib docs.
This needs som customization in terms of fonts, color, etc., Ideally make these things configurable options upstream in pydata-sphinx-theme so that we can just set it in conf.py and the theme does the rest.

This will also need some disentangling of the current mpl.css for keeping parts we still need in a same or similar form (e.g. gallery layout, version box, ...).