`gh workflow run` not working in `scheduled_builds.yml`

[ConorMacBride]

Provide a general description of the issue or problem.

The scheduled_builds.yml workflow which runs on a schedule on the main branch runs the ci.yml workflow on all the branches using the following commands:

gh workflow run ci.yml --repo sunpy/sunpy --ref main
gh workflow run ci.yml --repo sunpy/sunpy --ref 3.1
gh workflow run ci.yml --repo sunpy/sunpy --ref 3.0

However, even through the scheduled_builds.yml workflow runs successfully, no ci.yml workflows are actually run. It's strange that the command doesn't produce any output. The default GitHub Action token should have write access to Actions, so should not be a permissions issue.

Running locally using my GitHub token produces:

bash-3.2$ gh workflow run ci.yml --repo sunpy/sunpy --ref 3.1
✓ Created workflow_dispatch event for ci.yml at 3.1

To see runs for this workflow, try: gh run list --workflow=ci.yml

And the workflow is run as expected: https://github.com/sunpy/sunpy/actions/runs/2104531708

[ConorMacBride]

Maybe the default GITHUB_TOKEN isn't good enough? I can't see any other workflows which use the default token. For example:
https://github.com/github/codeql-variant-analysis-action/blob/1c0c2184a1f41116e7554553e9fec447541e000c/.github/workflows/integration-test-trigger.yml

[ConorMacBride]

In order to prevent recursion, any action using the GITHUB_TOKEN will never trigger a workflow. (https://docs.github.com/en/actions/using-workflows/triggering-a-workflow#triggering-a-workflow-from-a-workflow)

So we'll need to set a PAT instead, although I'm not sure if you can restrict those to specific repositories, so maybe a GitHub App (or use the Giles token)? The permissions it needs are detailed here: https://docs.github.com/en/rest/reference/actions#create-a-workflow-dispatch-event

See also #5811 which also needs a more permissive token to get working.