make streaks and the leaderboard live, and stop three AI chats from freezing the API

Found in a deeper pass over what the frontend's flow actually touches:

- Nothing in the app ever wrote StreakRecord: "days in a row" was 0 forever
  for every real user. Answers and lesson/island completions now record the
  day (Tehran time); a broken chain shows 0. A streak error never fails the
  answer itself.
- /api/leaderboard only changed when someone ran rebuild_leaderboard by
  hand. It is now computed live (60s cache); weekly counts island XP too.
- gunicorn ran 3 sync workers with a 30s timeout, so every "ask Pi" stream
  pinned a whole worker (~10s, GapGPT buffers the answer) and three at once
  queued the entire API. gunicorn.conf.py (read automatically from the
  working directory) switches to gthread, 8 threads, 120s timeout.
- Every /api/ response now says Cache-Control: private, no-store, so turning
  on caching in the ArvanCloud panel can never serve one student another's data.
- /api/user/summary named no active plan ever ("subscription app not
  implemented yet" had long stopped being true).

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

docs/operations.md

@@ -106,6 +106,7 @@ curl https://api.math.tadrisino2.ir/api/health
 | `CACHE_URL` | سرویس بالا می‌آید ولی نرخ بینِ workerها مشترک نیست؛ `/api/health` هشدار می‌دهد |
 | `KAVENEGAR_API_KEY` | `POST /api/auth/otp/request` خطای صریحِ `503` می‌دهد، نه موفقیتِ ساختگی |
 | `ZARINPAL_MERCHANT_ID` | مسیرِ پرداخت fail-closed می‌ماند (`503`) |
+| `gunicorn.conf.py` (در ریپو، نه env) | gunicorn خودش از پوشه‌ی کاری می‌خواندش: workerهای `gthread` با ۸ نخ و timeoutِ ۱۲۰. بدونِ آن، سه استریمِ هم‌زمانِ دستیار کلِ API را قفل می‌کرد |
 | `FRONTEND_URL` · `ZARINPAL_REDIRECT_URL` | بعد از پرداخت کاربر به `https://math.tadrisino2.ir/?orderId=…&status=paid\|failed` برمی‌گردد. `ZARINPAL_REDIRECT_URL=-` یعنی همان پاسخِ JSONِ قدیمی |
 | `OPENAI_API_KEY` · `QDRANT_API_KEY` | `POST /api/ai/ask` همان پاسخِ stub را می‌دهد |
 | `TEST_LOGIN_PHONES` | هیچ حسابِ تستی باز نیست (بخشِ بعد) |