GitLab: Make commit in (shared) CI runner and push to repository/open merge request
CI token used for code checkout is not allowed to do writes to the git repository (unlike GitHub Actions). You need to generate a new personal token and add it to secrets.
See our integration project here as a sample: https://gitlab.com/taleodor/sample-helm-cd
Note, if you search through StackOverflow, you may find several other ways to achieve this but in any case you need to explicitly pass valid credentials that are able to write to the repo.