Stage 12: observability & performance (OTel/OTLP, domain metrics, guest GC)

- pkg/telemetry: shared OTel provider bootstrap (none/stdout/otlp + W3C
  propagators + Go runtime metrics); backend/internal/telemetry becomes a thin
  facade keeping its gin middleware.
- Telemetry parity: gateway and the Telegram connector gain telemetry runtimes
  and config (GATEWAY_/TELEGRAM_ SERVICE_NAME + OTEL_*); otelgrpc instruments the
  backend push server, the gateway's backend+connector clients and the connector
  server. Default exporter stays none (collector/dashboards are Stage 14).
- Operational metrics (variant attribute on game-scoped ones): game_replay_duration,
  game_move_validate_duration, games_started_total, games_abandoned_total,
  game_cache_active, chat_messages_total{kind}, gateway edge_request_duration.
  Wired via the SetMetrics setter pattern (default no-op meter).
- TODO-3: account.GuestReaper deletes guests with no game seat past
  BACKEND_GUEST_RETENTION (default 30d, swept every BACKEND_GUEST_REAP_INTERVAL).
- Tests: pkg/telemetry exporter selection; game/social/edge metric recording via
  a manual reader; config (otlp accepted, guest knobs); inttest guest reaper.
- Docs: PLAN.md re-scopes Stage 12 and adds Stage 13 (alphabet-on-wire) + Stage 14
  (CI/deploy) with the agreed dictionary-versioning resolution; ARCHITECTURE 11/13,
  TESTING, the three READMEs and FUNCTIONAL(+ru) updated.

backend/internal/game/service.go

@@ -33,6 +33,7 @@ type Service struct {
 	clock    func() time.Time
 	rng      func() int64
 	pub      notify.Publisher
+	metrics  *gameMetrics
 	log      *zap.Logger
 }
 
@@ -51,6 +52,7 @@ func NewService(store *Store, accounts *account.Store, registry *engine.Registry
 		clock:    clock,
 		rng:      randomSeed,
 		pub:      notify.Nop{},
+		metrics:  defaultGameMetrics(),
 		log:      log,
 	}
 }
@@ -135,7 +137,8 @@ func (svc *Service) Create(ctx context.Context, params CreateParams) (Game, erro
 	if err := svc.store.CreateGame(ctx, ins, params.Seats); err != nil {
 		return Game{}, err
 	}
-	svc.cache.put(id, g)
+	svc.cache.put(id, g, params.Variant.String())
+	svc.metrics.recordStarted(ctx, params.Variant)
 	return svc.store.GetGame(ctx, id)
 }
 
@@ -350,6 +353,7 @@ func (svc *Service) timeoutGame(ctx context.Context, gameID uuid.UUID, now time.
 	if _, err := svc.commit(ctx, gameID, g, rec, "timeout", rackBefore, nil, cur.Seats); err != nil {
 		return false, err
 	}
+	svc.metrics.recordAbandoned(ctx, cur.Variant)
 	return true, nil
 }
 
@@ -373,7 +377,9 @@ func (svc *Service) EvaluatePlay(ctx context.Context, gameID, accountID uuid.UUI
 	if err != nil {
 		return EvalResult{}, err
 	}
+	validateStart := time.Now()
 	rec, err := g.EvaluatePlay(dir, tiles)
+	svc.metrics.recordValidate(ctx, pre.Variant, validateStart)
 	if err != nil {
 		if errors.Is(err, engine.ErrIllegalPlay) {
 			return EvalResult{Valid: false}, nil
@@ -704,7 +710,7 @@ func (svc *Service) liveGame(ctx context.Context, pre Game) (*engine.Game, error
 		return nil, err
 	}
 	if !g.Over() {
-		svc.cache.put(pre.ID, g)
+		svc.cache.put(pre.ID, g, pre.Variant.String())
 	}
 	return g, nil
 }
@@ -713,6 +719,7 @@ func (svc *Service) liveGame(ctx context.Context, pre Game) (*engine.Game, error
 // re-applying every journalled move in order. The deterministic bag makes the
 // reconstruction exact.
 func (svc *Service) replay(ctx context.Context, pre Game) (*engine.Game, error) {
+	defer svc.metrics.recordReplay(ctx, pre.Variant, time.Now())
 	seed, err := svc.store.GameSeed(ctx, pre.ID)
 	if err != nil {
 		return nil, err