Record that a batch of approved earnings has actually been disbursed.

This is the ledger's record that money moved; it does not move money. The transfer is a treasury operation, and payout_batch_id is how the two are reconciled — GET /admin/earnings?payout_batch_id=... returns exactly the rows a given disbursement covered.

user_id appears here and nowhere else on this router. That is the point of the split: every doctor-facing route scopes from the session and cannot name another physician, and the one route that must name one is admin-gated.