A scheduled or webhook run acts as the agent's owner with no one to
approve, so a public-link user or API-key caller could have the agent
schedule a write and have it run on the owner's accounts. Runs now keep
the caller's rules: a schedule set by someone who reaches the agent only
by its public link runs as a public-link caller, one set through the API
(recorded as created_via 'api', migration 0042) and every webhook run as
an external caller, each with the agent's API write allowlist.