CI breaks when tagging a release, requiring a manual PR to fix

# Problem

For example: https://github.com/apache/buildstream/pull/2175

Breaks unrelated work: https://github.com/apache/buildstream/pull/2172#issuecomment-5316243544

## Definition of Done

- [ ] Reason failure is more transparent(as proposed https://github.com/apache/buildstream/pull/2175#discussion_r3796604725)
- [ ] Investigate and implement a more streamline process if possible (https://github.com/apache/buildstream/pull/2175#discussion_r3796703622)

Start with the failing release-tag workflow and compare the examples in pull requests 2175 and 2172, including the linked discussion. Trace why tagging a release breaks unrelated work. Done means the failure reason is more transparent and, if feasible, the release process no longer requires a manual PR.

Written by the indexing model from the issue text.