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/sync/leases.py

@@ -20,6 +20,8 @@ from app.redis_client import aw
 LIVE_SET = "sync:live"
 _LEASE_PREFIX = "sync:lease:"
 WORKERS_PREFIX = "sync:workers:"
+_TIER_PREFIX = "sync:tier:"
+_SESSION_PREFIX = "sess:active:"
 
 
 def lease_key(account_id: uuid.UUID) -> str:
@@ -30,6 +32,20 @@ def worker_key(worker_id: str) -> str:
     return f"{WORKERS_PREFIX}{worker_id}"
 
 
+def tier_key(account_id: uuid.UUID) -> str:
+    return f"{_TIER_PREFIX}{account_id}"
+
+
+def session_key(user_id: uuid.UUID | str) -> str:
+    """Presence key the API refreshes while a user has an active session (§5)."""
+    return f"{_SESSION_PREFIX}{user_id}"
+
+
+async def mark_user_active(redis: aioredis.Redis, user_id: uuid.UUID | str, grace_s: int) -> None:
+    """Refresh the user's session-heat key; workers read it for tier promotion."""
+    await aw(redis.set(session_key(user_id), "1", ex=grace_s))
+
+
 # Renew only if we still own the lease (guards against a stale worker extending a
 # lease another worker has already claimed after expiry). Returns 1 on success.
 _RENEW_LUA = """