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.

gateway/cmd/gateway/main.go

@@ -26,11 +26,14 @@ import (
 	"scrabble/gateway/internal/ratelimit"
 	"scrabble/gateway/internal/session"
 	"scrabble/gateway/internal/transcode"
+	pkgtel "scrabble/pkg/telemetry"
 )
 
 const (
 	// shutdownTimeout bounds the graceful HTTP shutdown.
 	shutdownTimeout = 10 * time.Second
+	// telemetryShutdownTimeout bounds the OpenTelemetry flush during process exit.
+	telemetryShutdownTimeout = 5 * time.Second
 	// pushReconnectDelay is the pause before re-subscribing to the backend push
 	// stream after it ends.
 	pushReconnectDelay = 2 * time.Second
@@ -63,6 +66,21 @@ func run(ctx context.Context, cfg config.Config, logger *zap.Logger) error {
 	ctx, cancel := context.WithCancel(ctx)
 	defer cancel()
 
+	tel, err := pkgtel.New(ctx, cfg.Telemetry)
+	if err != nil {
+		return err
+	}
+	defer func() {
+		shutdownCtx, sc := context.WithTimeout(context.Background(), telemetryShutdownTimeout)
+		defer sc()
+		if err := tel.Shutdown(shutdownCtx); err != nil {
+			logger.Warn("telemetry shutdown", zap.Error(err))
+		}
+	}()
+	if err := tel.StartRuntimeMetrics(); err != nil {
+		logger.Warn("telemetry: start runtime metrics", zap.Error(err))
+	}
+
 	backend, err := backendclient.New(cfg.BackendHTTPURL, cfg.BackendGRPCAddr, cfg.BackendTimeout)
 	if err != nil {
 		return err
@@ -109,6 +127,7 @@ func run(ctx context.Context, cfg config.Config, logger *zap.Logger) error {
 		Heartbeat:  cfg.PushHeartbeatInterval,
 		Logger:     logger,
 		AdminProxy: adminProxy,
+		Meter:      tel.MeterProvider().Meter("scrabble/gateway/edge"),
 	})
 
 	// Bridge the backend push stream into the fan-out hub (and the out-of-app