Caching code for CI is too duplicated

[alice-i-cecile]

We have a ton of copy-pasted cache code so every adjustment or fix has to touch a lot of places and you're bound to miss one at some point.

I strongly suggest we create a composite action for that, which could be done directly in this repo, in .github/actions.
But if you want, it can be tackled in a separate PR :)

Originally posted by @TimJentzsch in #20144 (comment)