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.

platform/telegram/cmd/telegram/main.go

@@ -12,11 +12,14 @@ import (
 	"net"
 	"os/signal"
 	"syscall"
+	"time"
 
+	"go.opentelemetry.io/contrib/instrumentation/google.golang.org/grpc/otelgrpc"
 	"go.uber.org/zap"
 	"google.golang.org/grpc"
 
 	telegramv1 "scrabble/pkg/proto/telegram/v1"
+	pkgtel "scrabble/pkg/telemetry"
 	"scrabble/platform/telegram/internal/bot"
 	"scrabble/platform/telegram/internal/config"
 	"scrabble/platform/telegram/internal/connector"
@@ -24,6 +27,9 @@ import (
 	"scrabble/platform/telegram/internal/loginwidget"
 )
 
+// telemetryShutdownTimeout bounds the OpenTelemetry flush during process exit.
+const telemetryShutdownTimeout = 5 * time.Second
+
 func main() {
 	cfg, err := config.Load()
 	if err != nil {
@@ -46,6 +52,21 @@ func main() {
 // run wires the bot and the gRPC server and serves both until the context is
 // cancelled.
 func run(ctx context.Context, cfg config.Config, logger *zap.Logger) error {
+	tel, err := pkgtel.New(ctx, cfg.Telemetry)
+	if err != nil {
+		return err
+	}
+	defer func() {
+		shutdownCtx, cancel := context.WithTimeout(context.Background(), telemetryShutdownTimeout)
+		defer cancel()
+		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))
+	}
+
 	b, err := bot.New(bot.Config{
 		Token:      cfg.BotToken,
 		APIBaseURL: cfg.APIBaseURL,
@@ -60,7 +81,7 @@ func run(ctx context.Context, cfg config.Config, logger *zap.Logger) error {
 		loginwidget.NewHMACValidator(cfg.BotToken),
 		b, cfg.GameChannelID, logger)
 
-	grpcServer := grpc.NewServer()
+	grpcServer := grpc.NewServer(grpc.StatsHandler(otelgrpc.NewServerHandler()))
 	telegramv1.RegisterTelegramServer(grpcServer, srv)
 
 	lis, err := net.Listen("tcp", cfg.GRPCAddr)