workflow/tests: move Docker tests to docker.yml

[ZhongRuoyu]

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It's more intuitive that way.

Resolves #17827 (comment).

[MikeMcQuaid]

Looks good, thanks for cleanup @ZhongRuoyu!

A nice follow-up would be to migrate to using https://github.com/docker/build-push-action

I can DM you how Workbrew uses this if that'd be useful but TL;DR you can get better caching and push with less conditional logic required.