I'm a little confused about marking this as experimental? Isn't this the only way to manage the colormap registry? Or is your point that the access methods etc are experimental, but the old API still exists?

Yes, the old API still exists. On the dev call we decided to be on the safe side and mark the new API as experimental to still have the freedom to change everything.

Dee also the transition path in #20853.

subplots_mosaic is tagged provisional(https://matplotlib.org/devdocs/tutorials/index.html#provisional) so should there be some sort of consistency?

I was following th "experimental" terminology from scipy. Also to me, "provisional" sounds unfinished and not in the final state. Indeed:

provisional: for the present time but likely to change:

https://dictionary.cambridge.org/dictionary/english/provisional

It's unlikely but possible that the ColormapRegistry changes, so provisional is not the right term.

So then should the section of the tutorials subplot mosaic is in change to experimental? Either word indicates that the API isn't final?

I think so. Both indicate not final, but in my understanging "provisional" = likely to change; "experimental" = might still change. But that should be re-checked by native speakers.

We have been using "experimental" for years now, so should probably stick to that?

We have been using both, but more often "experimental":

experimental: 36 hits
https://matplotlib.org/devdocs/search.html?q=experimental#

provisional: 10 hits
https://matplotlib.org/devdocs/search.html?q=provisional#

@dstansby I've clarified what experimental means here.