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/config.py

@@ -29,7 +29,6 @@ class Settings(BaseSettings):
     meili_key: str = Field(default="", alias="MEILI_KEY")
 
     undo_seconds: int = Field(default=10, alias="UNDO_SECONDS")
-    poll_interval: int = Field(default=120, alias="POLL_INTERVAL")
     session_ttl_days: int = Field(default=30, alias="SESSION_TTL_DAYS")
     max_attachment_mb: int = Field(default=25, alias="MAX_ATTACHMENT_MB")
     log_level: str = Field(default="INFO", alias="LOG_LEVEL")
@@ -44,6 +43,13 @@ class Settings(BaseSettings):
     max_accounts_per_worker: int = Field(default=400, alias="MAX_ACCOUNTS_PER_WORKER")
     lease_ttl: int = Field(default=60, alias="LEASE_TTL")
     lease_renew: int = Field(default=20, alias="LEASE_RENEW")
+    # Activity tiers (§5): hot = persistent IDLE, warm/cold = transient polls.
+    poll_warm: int = Field(default=180, alias="POLL_WARM")
+    poll_cold: int = Field(default=900, alias="POLL_COLD")
+    tier_hot_activity_h: int = Field(default=24, alias="TIER_HOT_ACTIVITY_H")
+    tier_session_grace_min: int = Field(default=30, alias="TIER_SESSION_GRACE_MIN")
+    tier_cold_after_d: int = Field(default=3, alias="TIER_COLD_AFTER_D")
+    hot_budget_per_worker: int = Field(default=250, alias="HOT_BUDGET_PER_WORKER")
 
     oauth_google_client_id: str = Field(default="", alias="OAUTH_GOOGLE_CLIENT_ID")
     oauth_google_client_secret: str = Field(default="", alias="OAUTH_GOOGLE_CLIENT_SECRET")