Remove publish job from the check workflow

[kemzeb]

This appears to be a job that existed before we began publishing new releases using PyPI's trusted publisher feature in release.yml.

From exploring the Actions/Deployments tab, I could not find an instance where this job was ran. Seeing the check workflow configuration, we ignore all tag push events because of the tags-ignore usage. This would mean that publish will always be skipped since we don't listen for tag pushes in the check workflow. We also no longer have a pypi_password secret so even if it were to run it should fail.

I also decided to just remove the tags-ignore as according to the docs (though the wording is a tad weird), tag push events won't trigger a workflow run if we specify only branch.