Sync now: the presser's own matters and the firm's lists in, the deliveries' states back (billing, admin)

Sync now, as the person who pressed it means it, run inside this request and answered when it ends. For a practice system each member signs in to (tenant.connector.identity is sign_in on GET /v1/me) it is the CALLER'S OWN sync: their complete list of matters compared with the system, what changed in them, and the firm's shared lists when those are due; it never reads as a colleague and never waits on one, and a caller who is not signed in to the system syncs nothing. For a system the firm connected once it is the firm's sync, compared whole. It is also the request a client sends straight after PUT /v1/connector answered, since a connect syncs nothing itself: a connector that still waits on its team step (pending_mapping) is read exactly as a connected one, so the firm's first read runs here, with progress, before anybody pressed Done, and its status stays pending_mapping. While it runs, GET /v1/connector/sync/progress says how far it is. Where a sync of the same subject is already running (the scheduled run has the firm, or the caller), this request WAITS for it, up to a minute, and then makes its own, so the answer is a sync that happened; one it cannot outwait is answered with an error saying a sync is still running and zero counts, never as a sync in which nothing changed, and the progress route goes on saying running. It pushes nothing: an entry is released only once the practice system has taken it, inside the release. A failure is reported in the answer's error and on the connector row rather than as a status code: the run happened, and what it could not do is what the report is for. deliveries is answered with zero counts: what the practice system did with released entries is measured, never shown to the firm (R-8). A firm connected to a system this service carries no adapter for answers the not-available 422. On the operator's mount it is the firm's whole run: every signed-in member, as the scheduler runs it.