refactor(quota): own the quota session; Plex per-section commit (R6 S2)

Transaction ownership (C-A5):
- quota.record_usage / log_action write in their OWN SessionLocal(), committed
  immediately, and no longer take/commit the caller's db. The spend stays DURABLE
  regardless of the caller (read-only YouTube paths never commit; a failed job rolls
  back) — under-counting the shared daily budget would risk overspending the real
  YouTube quota — AND quota stops flushing a job's partial state mid-run behind its
  own `except: db.rollback()`. units_used_today switches to a scalar SELECT so
  measured()'s before/after diff sees the separate session's commits (READ COMMITTED).
  Call sites updated (youtube/client.py ×3, routes/search.py ×1).
- plex sync commits PER SECTION (moved the end-of-loop commit inside), so a PlexError
  on a later library keeps the ones already mirrored (idempotent; next run reconciles).

The sync jobs did NOT rely on record_usage's incidental commit for persistence — their
per-item functions (apply_rss_feed, backfill_channel_recent, import_subscriptions,
sync_user_playlists, apply_channel_autotags) all commit internally, so the in-loop
rollback handlers already isolate a failed item. No loop restructuring needed.

DB-lane tests (test_quota_ownership, 4): spend survives a caller rollback while the
caller's uncommitted row does NOT leak; accumulation; measured-style mid-txn read.
Gate: ruff clean; DB lane 180 green.

backend/app/plex/sync.py

@@ -129,7 +129,10 @@ def sync(db: Session) -> dict:
                 else:
                     _sync_shows(db, plex, lib, stats)
                 _sync_collections(db, plex, lib, stats)
-            db.commit()
+                # Commit each section as it completes: a PlexError on a LATER section then keeps the
+                # libraries already mirrored (idempotent — the next run reconciles the rest), instead
+                # of the old single end-of-loop commit that a late failure rolled back entirely.
+                db.commit()
             # Rich-fetch a bounded batch of not-yet-enriched titles' FULL cast, so the whole library
             # becomes filterable over successive runs (the cheap listing above only stored the top ~3).
             try: