What worked well for me (worked with GitHub, self hosted BitBucket, most likely will work on GitLab too).
Pre-requisites
Note, that despite the name, password here is your access token generated by GitHub and NOT your GitHub password.
from git import Repo
full_local_path = "/path/to/repo/"
username = "your-username"
password = "your-password"
remote = f"https://{username}:{password}@github.com/some-account/some-repo.git"
Clone repository
This will store your credentials in .git/config, you won’t need them later.
Repo.clone_from(remote, full_local_path)
Commit changes
repo = Repo(full_local_path)
repo.git.add("rel/path/to/dir/with/changes/")
repo.index.commit("Some commit message")
Push changes
As mentioned above, you don’t need your credentials, since they are already stored in .git/config.
repo = Repo(full_local_path)
origin = repo.remote(name="origin")
origin.push()