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>

content/migrations/0013_alter_userlessoncompletion_created_at_and_more.py

@@ -0,0 +1,23 @@
+# Generated by Django 5.2.17 on 2026-10-11 16:33
+
+from django.db import migrations, models
+
+
+class Migration(migrations.Migration):
+
+    dependencies = [
+        ('content', '0012_choice_value_300'),
+    ]
+
+    operations = [
+        migrations.AlterField(
+            model_name='userlessoncompletion',
+            name='created_at',
+            field=models.DateTimeField(auto_now_add=True, db_index=True),
+        ),
+        migrations.AlterField(
+            model_name='usernodecompletion',
+            name='created_at',
+            field=models.DateTimeField(auto_now_add=True, db_index=True),
+        ),
+    ]