It depends on what kind of event you want to trigger. The point of the documentation that says
GITHUB_TOKEN won’t trigger new workflows is that regular repository activity (e.g. pushing a new commit) authenticated with the
GITHUB_TOKEN won’t cause additional workflows listening for that kind of event to run.
The documentation for the action you linked says it creates a “repository dispatch” event. The documentation for the create a repository dispatch event API endpoint says:
This endpoint requires write access to the repository by providing either:
I don’t know the action, so please consider whether you trust it enough to give it the kind of privileges that go with the