Postgres connection pool, clean 503 under overload, time indexes, 4 workers

Postgres here allows 60 connections, but each of the 96 gunicorn threads held its
own persistent one: at 100 concurrent users (local Postgres with the same limit)
21% of requests were 500 "remaining connection slots are reserved". Now each worker
has a psycopg pool (8), so the same load gives 0 errors and 714 req/s (was 460).

- A full pool answers 503 + Retry-After (DRF handler and middleware), not 500.
- The AI tutor and the OTP SMS call return their connection before the network wait.
- statement_timeout 30 s, idle-in-transaction 60 s; bad pool settings and the old
  DB_CONN_MAX_AGE stop startup instead of failing every request.
- /api/health dbPool: per-worker pool stats and workers x pool + 6 vs max_connections.
- Indexes on the columns global counters filter by time (weekly leaderboard,
  global SMS cap, global AI cap); the leaderboard recomputes once per expiry.
- Worker count moves into gunicorn.conf.py (4 on a shared 8-core box).
- security doc: Redis item closed (server uses our own Redis since 2026-10-08).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

progress/tests_leaderboard_cache.py

@@ -0,0 +1,43 @@
+"""
+کشِ لیدربورد بی «ازدحامِ لحظه‌ی انقضا» (progress/leaderboard.py، cached_scores): وقتی کش منقضی می‌شود
+فقط یک درخواست جدول را از نو حساب می‌کند و بقیه آخرین نسخه را می‌گیرند. هم‌زمانیِ واقعی بینِ workerها
+آزموده نشده؛ این تست‌ها قفل را با گذاشتنِ دستیِ کلیدش شبیه‌سازی می‌کنند.
+"""
+from unittest import mock
+
+from django.core.cache import cache
+from django.test import SimpleTestCase
+
+from progress import leaderboard
+
+
+class CachedScoresTests(SimpleTestCase):
+    def setUp(self):
+        cache.clear()
+
+    def test_first_call_computes_and_fills_both_copies(self):
+        with mock.patch.object(leaderboard, 'compute_scores', return_value=[(1, 50)]) as compute:
+            self.assertEqual(leaderboard.cached_scores('weekly'), [(1, 50)])
+            self.assertEqual(leaderboard.cached_scores('weekly'), [(1, 50)])
+        compute.assert_called_once_with('weekly')
+        self.assertEqual(cache.get('leaderboard:weekly:stale'), [(1, 50)])
+        self.assertIsNone(cache.get('leaderboard:weekly:lock'))
+
+    def test_while_someone_else_recomputes_the_stale_copy_is_served(self):
+        cache.set('leaderboard:weekly:stale', [(2, 30)], 600)
+        cache.set('leaderboard:weekly:lock', 1, 30)
+        with mock.patch.object(leaderboard, 'compute_scores') as compute:
+            self.assertEqual(leaderboard.cached_scores('weekly'), [(2, 30)])
+        compute.assert_not_called()
+
+    def test_without_any_copy_it_computes_even_if_locked(self):
+        cache.set('leaderboard:weekly:lock', 1, 30)
+        with mock.patch.object(leaderboard, 'compute_scores', return_value=[(3, 10)]) as compute:
+            self.assertEqual(leaderboard.cached_scores('weekly'), [(3, 10)])
+        compute.assert_called_once()
+
+    def test_a_failed_recompute_releases_the_lock(self):
+        with mock.patch.object(leaderboard, 'compute_scores', side_effect=RuntimeError('db')):
+            with self.assertRaises(RuntimeError):
+                leaderboard.cached_scores('weekly')
+        self.assertIsNone(cache.get('leaderboard:weekly:lock'))