Unable to git checkout to specific branch in git submodule

I am trying to achieve something that I am not sure is possible. I haven't been able to find any similar cases to mine, which is why I am creating this issue. The goal is to see if anyone has encountered this before and knows how to resolve it. I wouldn't say it's a problem per se, just a request for help.

Context

My repository has two git submodules and looks like this:

/src
/submodule_1
/submodule_2

My use case is a bit special because the repository is closely related to one of the git submodules. From now on, I will only mention the "git submodule" and ignore the other one since none of this concerns the other.

Basically, my workflow is triggered by pull requests, and I need to be able to clone the submodule and checkout to a branch with the same name (if a branch with the same name does not exist, master should be used).

This is how I try to checkout in the submodule:

cd submodule_folder
git fetch --all
git merge origin/master
# Try to checkout to branch with same name or master if it does not exist
git checkout -b "origin/$GITHUB_HEAD_REF" 2>&1 | grep -wi 'fatal' && git checkout master
git pull

Then after that, I need to execute some script from that submodule. The problem is I can't checkout to the branch I want (The branch exists in the origin of the git submodule repository, double-checked).

Action configuration:

# ....
# ....
steps:
  - uses: actions/checkout@v3
    with:
       submodules: recursive
       token: ${{ secrets.ACCESS_TOKEN }}

Start with the actions/checkout@v3 step and the submodule checkout commands shown in the issue. Check how recursive submodules are initialized and whether the action exposes an entry point for selecting a submodule branch. Done means a reproducible workflow checks out the matching submodule branch and falls back to master when it is absent.