chore: fix release-to-publish workflow

[wangela]

1. The release worfklow is failing because the call to the publish workflow requires checkout first, which must not be handled under a separate conditional.

2. Release Please is unable to distinguish between version numbers of this package that should be bumped up with each release vs other strings that represent version numbers but shouldn't be bumped. This causes an extra manual commit on the release PR to correct the edits that release-please makes. Since the README has 3 strings that shouldn't be bumped and 1 instance that should be bumped, we will manually update the bump until Release Please can support a more detailed regex (feature request in Support custom regex for x-release-please-* annotations in extra-files googleapis/release-please#2345)

• Make sure to open a GitHub issue as a bug/feature request before writing your code! That way we can discuss the change, evaluate designs, and agree on the general idea
• Ensure the tests and linter pass
• Code coverage does not decrease (if any source code was changed)
• Appropriate docs were updated (if necessary)