[Regression] Can't delete MR branches created prior to GitLab 13.8.1

Summary

Our last GitLab upgrade led to the regression that we can't delete branches created prior to the migration, and that by any means.

Steps to reproduce

1. Have a GitLab installation prior to 13.8.1 with a configured git repo
2. Create a branch out of master
3. Add a commit on top
4. Push the branch to the origin
5. Create a MR based on it
6. Upgrade GitLab to 13.8.1
7. Tick the box so that the source branch is deleted when merged to master
8. Merge

Example Project

Any.

What is the current bug behavior?

1. The source branch is not deleted.
2. Doing it manually from the UI doesn't work either.
3. Doing it from the command line doesn't work either:

   git push -d origin $my_source_branch
   error executing git hookfatal: ref updates aborted by hook

   (the git client waits forever until interrupted)

What is the expected correct behavior?

The source branch is deleted by any of the 3 above means.

GitLab environment info

GitLab Enterprise Edition 13.8.1-ee