I don't especially understand the workflow that was envisioned with the tagging user interface. It behaves as you've described it. The tags are written into the git repository in the workspace. That assumes the workspace is persistent (which is not a valid assumption with many of the cloud agent providers).
I don't recall if the tag is created in the most recently used workspace, or the workspace that was used for the specific job. Since jobs may run on a different agent each time, the workspace may be different each time.
If you want to tag a build, it may be better to use a parameterized Pipeline job with the proposed tag name as the argument. Then apply the tag during the Pipeline job and immediately push it to the remote repository.
Mark Waite