Update release automation so that 'push a tag' is the only action needed

Let's update this repo to match https://github.com/bazel-contrib/rules-template

The release automation is completely performed in a standard, shared GitHub Actions reusable workflow.

As rule maintainers, this reduces the possibility we can make a mistake during a release, and improves security by allowing GitHub Actions to fully verify the release artifacts. In fact, we'll be able to add some SLSA-style attestation to the bazel-contrib/rules-template in a couple weeks.

It also reduces the maintenance burden for the repo to the minimum necessary, which is important for its long term health as individual engineers get pulled into other things.

Compare this repository's existing release automation with the bazel-contrib/rules-template repository, focusing on its standard shared GitHub Actions reusable workflow. Verify how a release is triggered by pushing a tag and confirm that the workflow performs the release and artifact verification without additional manual actions.

Written by the indexing model from the issue text.