The technique this tool uses for checking out tags only preserves the relation between tag and ref, not any annotations created with git tag -a.

git fetch origin +$HASH:refs/tags/$TAG
git checkout -f refs/tag/$TAG

I have a CI action that depends on information from annotated tags. Specifically, the name of the person who applied the tag: git tag --list --points-at HEAD --format '%(taggeremail)' (I can't use ${{ github.actor }} for reasons).

The workaround is to run git fetch -f origin ${{ github.ref }}:${{ github.ref }}. But it would be better not to need this workaround.