that's my current setup, but it requires quite some manual work. Especially when I want to release. ie I commit and push to private repo, create PR with summary, merge. Then I run the script to copy over files to public repo (skipping files listed in a custom .publicignore file), then manually commit to public repo (I have to copy over commit messages and PR summaries from private repo), then push and release on public. It's a bit exahusting, and when something drifts it becomes a hell to keep them both in sync.
My suggestion was to keep one repo with the docs and a separate repo with the code, and zero intersection.
I teletransported commits from one repo to another with "git format-patch" and "git am" or something like that. I never remember the magic spell. If you do that too often, you may automate it in a script.