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/views.py

@@ -15,6 +15,8 @@ from rest_framework.response import Response
 from rest_framework.throttling import BaseThrottle, ScopedRateThrottle
 from rest_framework.views import APIView
 
+from config.db import release_db_connection
+
 from .authentication import invalidate_user_cache, issue_access_token
 from .models import LoginEvent, OTPCode, Profile, Session, User, hash_refresh_token
 from .services import OTPDeliveryError, send_otp_sms
@@ -195,6 +197,9 @@ class RequestOTPView(APIView):
             # روزی چند درصد شانس داشت. فرانت تا ۶ رقم را می‌پذیرد.
             code = f'{secrets.randbelow(1_000_000):06d}'
             otp_row = OTPCode.objects.create(phone=phone, code=code, expires_at=now + ttl)
+        # کاوه‌نگار تا چند ثانیه طول می‌کشد؛ روزِ لانچ این پرترافیک‌ترین مسیر است و اتصالِ دیتابیس
+        # در این مدت به pool برمی‌گردد (config/db.py).
+        release_db_connection()
         try:
             send_otp_sms(phone=phone, code=code)
         except OTPDeliveryError: