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/celery_app.py

@@ -97,6 +97,10 @@ def make_celery() -> Celery:
                 "task": "backend.app.tasks.maintenance.prune_task_runs",
                 "schedule": 86400.0,  # daily
             },
+            "vacuum-analyze": {
+                "task": "backend.app.tasks.maintenance.vacuum_analyze",
+                "schedule": 604800.0,  # weekly — reclaim dead-tuple bloat + refresh stats
+            },
             "fc3h-backup-db-nightly": {
                 "task": "backend.app.tasks.backup.backup_db_nightly",
                 "schedule": 3600.0,  # hourly tick; task self-gates on configured UTC hour