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>

accounts/models.py

@@ -76,7 +76,9 @@ class Session(models.Model):
 class OTPCode(models.Model):
     phone = models.CharField(max_length=15, db_index=True)
     code = models.CharField(max_length=6)
-    expires_at = models.DateTimeField()
+    # ایندکس: سقفِ سراسریِ پیامکِ روزانه در هر درخواستِ کد کدهای ۲۴ ساعتِ اخیر را می‌شمارد
+    # (accounts/views.py)؛ ردیف‌ها پاک نمی‌شوند، پس بی‌ایندکس این شمارش با هر ورود کندتر می‌شد.
+    expires_at = models.DateTimeField(db_index=True)
     is_used = models.BooleanField(default=False)
     # تلاش‌های غلط روی همین کد. در دیتابیس شمرده می‌شود، نه در کشِ LocMem که
     # برای هر worker جداست؛ بعد از OTP_MAX_FAILED_ATTEMPTS کد باطل می‌شود.