The App token cannot update a run the job token created and vice versa, so
selecting runs by `app.slug === 'github-actions'` missed every App run: each
phase created another run, a published App success was never revoked, and a
head with an older job-token run made the App patch fail. Select runs by the
publishing app slug instead, pass `vars.DSH_APPROVAL_APP_SLUG`, and set the
external_id marker on the setup-phase run too.
Cover the App-owned update and the job-run coexistence, and align the note with
the measured earliest-suite rule and the App slug variable.
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