The [comment of @eftshift0](Rebasing all branches on new initial commit) pushed me into the right direction:

I've just rewritten the history using git-filter-repo, using this example script:

https://github.com/newren/git-filter-repo/blob/main/contrib/filter-repo-demos/insert-beginning

It does not create a new commit at the root of the repository, but just adds the file so it is available in every commit.