feat(maintenance): scheduled + manual DB VACUUM ANALYZE + bloat readout

The TABLESAMPLE showcase reads physical blocks (bloat-sensitive), and the
periodic prune/backfill/recovery tasks churn dead tuples faster than
autovacuum always keeps up — so explicit maintenance earns its keep here.

- tasks.maintenance.vacuum_analyze: VACUUM (ANALYZE) over high-churn tables
  (VACUUM_TABLES) on an AUTOCOMMIT connection (VACUUM can't run in a txn).
  Scheduled weekly via Beat; also operator-triggerable.
- _sync_engine.get_sync_engine(): expose the process engine for the
  autocommit connection.
- GET  /api/admin/maintenance/db-stats: per-table n_live/n_dead/dead_pct +
  last (auto)vacuum/analyze from pg_stat_user_tables — visibility, not a
  black box.
- POST /api/admin/maintenance/vacuum: enqueue the task on demand.

Tests: vacuum task runs + reports tables; db-stats shape; trigger queues.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

backend/app/tasks/_sync_engine.py

@@ -34,3 +34,10 @@ def sync_session_factory():
         )
         _SESSIONMAKER = sessionmaker(_ENGINE, expire_on_commit=False)
     return _SESSIONMAKER
+
+
+def get_sync_engine():
+    """The process-wide sync Engine — for raw work that needs a connection
+    directly (e.g. AUTOCOMMIT VACUUM, which can't run inside a transaction)."""
+    sync_session_factory()  # ensure _ENGINE is initialized
+    return _ENGINE