Cut /api/tasks/ p99 from ~2500ms toward ~150-300ms

Stack of optimizations against the same Hetzner→Neon transatlantic link.
The trace revealed every visible ms was network/proxy overhead — DB
execution itself is sub-millisecond per query (verified via EXPLAIN
ANALYZE: index scans on every hot path).

Connection layer:
- DB_HOST → Neon pooler endpoint (-pooler suffix). PgBouncer
  transaction-mode keeps backend Postgres connections warm so we no
  longer pay the ~110ms Postgres-startup RTT on cold queries.
- GORM pool tuned: MaxIdleConns 10→20, MaxLifetime 600s→1800s,
  MaxIdleTime added (default 0 = never close idle).
- Eager pool warm-up at boot via parallel pings — first user request
  no longer pays the ~440ms TCP+TLS+startup handshake.
- Redis maxmemory-policy noeviction → allkeys-lru. Cache writes will
  evict cold keys instead of erroring at the 256MB limit.

Auth layer:
- TokenCacheTTL 5min → 1 hour (Redis token cache).
- UserCacheTTL 30s → 5min (in-memory User cache, per pod).
- UserCache gains a 5,000-entry LRU cap so a flood of unique users
  can't blow up pod RSS. ~5MB worst-case per pod.
- Token + user lookup collapsed from 2 GORM Preload queries into a
  single INNER JOIN. Saves 1 RTT per cold-cache request.
- Auth middleware's m.db.* now use db.WithContext(ctx) so the SQL
  spans nest under the parent HTTP request in Jaeger.

Service layer:
- TaskService.ListTasks: replaced two-step
  FindResidenceIDsByUser → GetKanbanDataForMultipleResidences
  with a single GetKanbanDataForUser that uses a Postgres subquery
  for residence-access. One round-trip instead of two.
- New CacheService residence-IDs cache: \"residence_ids_user:<id>\"
  with 5-min TTL. Wired into Task/Residence/Contractor/Document
  services for the four hot read paths that need this list.
- Cache invalidation on every relevant mutation: CreateResidence,
  DeleteResidence, JoinWithCode, RemoveUser. DeleteResidence
  invalidates every member of the residence, not just the owner.

What this stacks up to (Hetzner→Neon, before US migration):
  Path                                 Before        After (target)
  Cache-warm authed read               ~800ms        ~100-200ms
  Cache-cold authed read (1st in 1hr)  ~2500ms       ~500-700ms
  First request after deploy           ~2500ms       ~700-900ms

The endgame US-region migration on top of this gets us to ~30-50ms
warm-cache, but we're shippable at ~150ms warm right now.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

internal/router/router.go

@@ -200,6 +200,15 @@ func SetupRouter(deps *Dependencies) *echo.Echo {
 	taskService.SetStorageService(deps.StorageService) // For reading completion images for email
 	subscriptionService := services.NewSubscriptionService(subscriptionRepo, residenceRepo, taskRepo, contractorRepo, documentRepo)
 	residenceService.SetSubscriptionService(subscriptionService) // Wire up subscription service for tier limit enforcement
+
+	// Wire Redis cache for residence-ID lookups across the four services that
+	// read it on the request hot path. Cache is best-effort; nil cache is OK.
+	if deps.Cache != nil {
+		residenceService.SetCacheService(deps.Cache)
+		taskService.SetCacheService(deps.Cache)
+		contractorService.SetCacheService(deps.Cache)
+		documentService.SetCacheService(deps.Cache)
+	}
 	taskTemplateService := services.NewTaskTemplateService(taskTemplateRepo)
 	suggestionService := services.NewSuggestionService(deps.DB, residenceRepo)