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/providers/base.py

@@ -85,7 +85,7 @@ class MailProvider(Protocol):
 
     async def idle(self, mailbox: str) -> None:
         """Blocks until the server signals change or 25 min elapse (re-issue IDLE). May raise
-        ProviderNotSupported => sync loop falls back to poll() every POLL_INTERVAL (default 120 s).
+        ProviderNotSupported => sync loop falls back to poll() every POLL_WARM (default 180 s).
         """
         ...