Disable staleness refresh GHA on release branches.

This non-hermetically broke for 25.x due to upgrade to Bazel 8 after github runner image update since this check doesn't use our bazel common image.

However, I don't think this was actually doing anything because of b/287117570 since we use staleness_check.yml presubmit and manually make staleness updates for release branches anyways.

https://github.com/protocolbuffers/protobuf/actions/runs/14577746819/job/40887512113

PiperOrigin-RevId: 749902868