[3.14] Forward-port 'check-abi' CI job from 3.13 (GH-133614)

Also add the python3.14.abi file as generated by the new job and remove
the 'main branch only' entry from .gitignore.

The only difference from the 3.13 job is the addition of `with.python-version: 3.x`
to the `setup-python` configuration to pacify a warning.