I was looking into a failed stable doc deployment and noticed that the action doc-deploy-stable is installing uv before performing a checkout of the repo. This shows the following warning in the logs

and I think this highlights that if a user wants to reuse uv cache, it will not work as expected because setup-uv does not have access to the information necessary for its cache management.
A simple fix should be to reorder the steps of the action. Note that this might also concern other actions and anyone handling this issue should have a look in the whole repo if possible :)