Don't run `check-crates-publishing` job on prs (#14064)

* Restore `check-crates-publishing-pipeline` job

This job was errorneously deleted in lieu of the
`check-crates-publishing` job.

This reverts commit 202836cb.

* Don't run `check-crate-publishing` job on prs.

Originally attempted in #14044. It's been broken for a while and we're
not sure yet how to move forward in the longer term.