If I understand correctly, the problem is that the docs are not published when the release branch is created, but only when a push is made to the release branch that modifies a file matching the on.push.paths filter. So what we really need is to trigger the workflow on the release branch creation. After that, it's fine to continue with the current behavior of only publishing when pushes are made to the release branch that modify a file matching the on.push.paths filter

I have an alternative proposal:
https://github.com/per1234/arduino-cli/commit/6d9bfd3ba70155ba7e2eace4edc58dd2a5511ad8

It uses the create event to trigger the workflow on every branch or tag creation. Unfortunately, the branches filter is not supported for this event. Also, filter patterns aren't supported in the jobs.<job_id>.if key. So the job will run on every branch or tag creation. The solution is to use a step with some bash code to do the filter:

RELEASE_BRANCH_REGEX="refs/heads/[0-9]+.[0-9]+.x"
if [[ "${{ github.event_name }}" == "push" || ( "${{ github.event_name }}" == "create" && "${{ github.ref }}" =~ $RELEASE_BRANCH_REGEX) ]]; then

then use the output of that job in the conditional of the publish job.

It's a little messy, but I think it's slightly better than maintaining duplicate workflows.

Let me know what you think.