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>

ai_tutor/views.py

@@ -16,6 +16,7 @@ from rest_framework.throttling import ScopedRateThrottle
 from rest_framework.views import APIView
 
 from accounts.models import User as AccountUser
+from config.db import release_db_connection
 from . import provider_status
 from .models import AskIdempotency, Conversation, Message, MessageFeedback
 from .serializers import (
@@ -471,6 +472,8 @@ class AskAIView(APIView):
                     answer_from_cache = True
                     _uncharge(user_message)
                 else:
+                    # Qdrant و مدل چند ثانیه طول می‌کشند؛ اتصالِ دیتابیس در این مدت به pool برمی‌گردد.
+                    release_db_connection()
                     used_chunks, retrieval_meta = retrieve_context(
                         _retrieval_query(v['userQuestion'], history, focus),
                         subject=subject, grade_id=grade_id,
@@ -610,6 +613,8 @@ class AskAIView(APIView):
                     _uncharge(user_message)
                     yield _sse('chunk', {'delta': answer_text})
                 else:
+                    # کلِ استریم (تا ۴۰ ثانیه) بی‌اتصالِ دیتابیس؛ ثبتِ پیامِ آخر یکی تازه قرض می‌گیرد.
+                    release_db_connection()
                     used_chunks, retrieval_meta = retrieve_context(
                         _retrieval_query(v['userQuestion'], history, focus),
                         subject=subject, grade_id=grade_id,