sync-v2 step 5: activity tiers (hot/warm/cold)

Each owned account is tiered by the coordinator; the runner shapes its work to
match — correctness identical, only latency/socket cost differ.

- hot: persistent INBOX IDLE + secondary poll every POLL_WARM.
- warm: no persistent socket; transient INBOX+special poll every POLL_WARM.
- cold: same transient poll every POLL_COLD.
- engine: poll_all_loop (transient full poll); secondary_poll_loop interval is
  now a parameter; POLL_INTERVAL removed in favor of POLL_WARM/POLL_COLD.
- coordinator: tier eval every 120s from session heat (sess:active:{user}) +
  recent mail (max internal_date within TIER_HOT_ACTIVITY_H), with the
  HOT_BUDGET_PER_WORKER guard shedding least-recently-active session-less hot
  accounts; user.active event promotes a user's accounts to hot at once (≤5s).
- API: login + WS connect/ping publish user.active and refresh sess:active
  (TTL TIER_SESSION_GRACE_MIN). New sync:tier:{id} key, default warm on claim.
- config: POLL_WARM/POLL_COLD/TIER_*/HOT_BUDGET_PER_WORKER.
- tests: 5 tier tests (session/recent-mail promotion, cold, user.active,
  budget demotion) alongside the lease/lifecycle acceptance tests.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

backend/app/ws.py

@@ -13,10 +13,12 @@ import logging
 
 from fastapi import APIRouter, WebSocket, WebSocketDisconnect
 
+from app.config import get_settings
 from app.events import get_event_bus
 from app.identity.cookies import SESSION_COOKIE_INSECURE, SESSION_COOKIE_SECURE
 from app.identity.sessions import resolve_session
 from app.redis_client import get_redis
+from app.sync import leases
 
 logger = logging.getLogger(__name__)
 
@@ -35,7 +37,9 @@ async def ws_endpoint(websocket: WebSocket) -> None:
 
     await websocket.accept()
     user_id = str(session.user_id)
-    # Sync v2 §3: an open WS means the user is active -> promote their tier.
+    grace_s = get_settings().tier_session_grace_min * 60
+    # Sync v2 §3/§5: an open WS means the user is active -> session heat + promote.
+    await leases.mark_user_active(get_redis(), user_id, grace_s)
     await get_event_bus().publish("user.active", {"user_id": user_id})
     pubsub = get_redis().pubsub()
     await pubsub.psubscribe("evt:*")
@@ -57,6 +61,8 @@ async def ws_endpoint(websocket: WebSocket) -> None:
             raw = await websocket.receive_text()
             try:
                 if json.loads(raw).get("type") == "ping":
+                    # A ping keeps the user's session heat alive (§5).
+                    await leases.mark_user_active(get_redis(), user_id, grace_s)
                     await websocket.send_json({"type": "pong"})
             except (ValueError, TypeError):
                 continue