Optimize Docker caching on CI

[Kobzol]

Currently, our GHA CI workflows on rust-lang/rust use a cached Docker build, which speeds up the workflow considerably. However, they still upload the resulting Docker image to the rust-lang-ci registry, even if there were no changes in the input Docker image. It would be nice to change that and avoid that needless upload in that case.

For reference, the caching was implemented in this PR: rust-lang/rust#119290.

[geektype]

As discussed, I'll have a look in to this over the weekend and submit a PR.