`doc-deploy-dev` action is not removing content created by `doc-deploy-pr` if `gh-pages` branch is not orphan

I believe that the `doc-deploy-dev` action is failing to remove the content created by the `doc-deploy-pr` action (subfolder in the `/pull` directory on the `gh-pages` branch, removed if the corresponding PR is closed) if the `gh-pages` branch is not orphan.

Here is a PR where I noticed it: https://github.com/ansys/pyaedt/pull/7983.
We had for some time set the `gh-pages` branch to not be orphan in PyAEDT and everyday, when a workflow executing the `doc-deploy-dev` action was run, a new comment was added to that closed PR: The action does notice that a subfolder on the `gh-pages` branch has to be removed, but fails at deleting it, so it's again finding it one the next day and posting that same comment again, etc !
For reference, here is a run where this happens: https://github.com/ansys/pyaedt/actions/runs/33831780194/job/100900831479
Note that the run is still returning success despite this.

My understanding is that the step named "Clean up pull/ directory if it exists" works just fine (hence the comments), but then there is something in the implementation of the `peaceiris/actions-gh-pages` that interferes with the deletion if the `gh-pages` branch has history. Somehow the change of deleting the folder is not pushed to the remote maybe?
Sorry that I cannot point to the exact root cause of this.
I can also confidently say that adding / removing the "deploy-pr-doc" badge (triggering the `doc-deploy-pr` action in PyAEDT) won't affect that behavior.

I understand this is a pretty corner case as `gh-pages` branches will most of the time be orphan (that branch is back to orphan in PyAEDT now), but still wanted to share that observation.

Begin with the doc-deploy-dev workflow and its "Clean up pull/ directory if it exists" step, then compare how doc-deploy-pr creates the subfolder and how peaceiris/actions-gh-pages publishes changes on a non-orphan gh-pages branch. Reproduce the behavior using the linked PyAEDT run and PR as references; done means closed PR subfolders are deleted remotely and the repeated comment no longer appears.

Written by the indexing model from the issue text.