Stage 6: gateway edge (Connect/FlatBuffers over h2c, platform/email/guest auth, sessions, rate-limit, admin passthrough, live push bridge)

New public ingress and the first network edge. Framework + a vertical slice of
operations end-to-end; remaining ops reuse the same transcode pattern in Stage 7.

Contracts (new module scrabble/pkg):
- push.proto (backend->gateway gRPC server-stream) + scrabble.fbs (FlatBuffers
  edge payloads), committed generated Go; buf/flatc Makefiles (dev-time codegen).

Backend:
- REST handlers on the /api/v1 groups: internal session endpoints
  (telegram/guest/email login -> mint, resolve, revoke) and the user slice
  (profile, submit_play, state, lobby enqueue/poll, chat).
- internal/notify in-process Publisher hub + internal/pushgrpc gRPC server
  (BACKEND_GRPC_ADDR) streaming your_turn/opponent_moved/chat/nudge/match_found;
  emission in game.commit, social, matchmaker.
- migration 00005 accounts.is_guest; guests are durable rows excluded from stats;
  ProvisionGuest; email-as-login (RequestLoginCode/LoginWithCode).

Gateway (new module scrabble/gateway):
- Connect Gateway service over h2c (Execute + Subscribe), FlatBuffers<->JSON
  transcode registry, Telegram initData HMAC validator (seam), session cache,
  token-bucket rate limiter (3 classes), push fan-out hub, backend REST + push
  gRPC client, admin Basic-Auth reverse proxy.

go.work: use ./pkg, ./gateway + replace scrabble/pkg. CI: gateway/**, pkg/**
path filters; unit build/vet/test span all three modules. Docs (PLAN,
ARCHITECTURE, FUNCTIONAL+ru, TESTING, READMEs) updated; gateway/pkg unit tests +
guest/email-login integration tests.

backend/internal/lobby/matchmaker.go

@@ -11,6 +11,7 @@ import (
 
 	"scrabble/backend/internal/engine"
 	"scrabble/backend/internal/game"
+	"scrabble/backend/internal/notify"
 )
 
 // Matchmaker is the in-memory auto-match pool: a FIFO queue per variant that pairs
@@ -30,6 +31,7 @@ type Matchmaker struct {
 	robots    RobotProvider
 	waitDelay time.Duration
 	clock     func() time.Time
+	pub       notify.Publisher
 	log       *zap.Logger
 
 	mu           sync.Mutex
@@ -51,6 +53,7 @@ func NewMatchmaker(games GameCreator, robots RobotProvider, waitDelay time.Durat
 		robots:       robots,
 		waitDelay:    waitDelay,
 		clock:        func() time.Time { return time.Now().UTC() },
+		pub:          notify.Nop{},
 		log:          log,
 		queues:       make(map[engine.Variant][]uuid.UUID),
 		queued:       make(map[uuid.UUID]engine.Variant),
@@ -60,6 +63,26 @@ func NewMatchmaker(games GameCreator, robots RobotProvider, waitDelay time.Durat
 	}
 }
 
+// SetNotifier installs the live-event publisher used to push match_found to the
+// seated players when a pairing or robot substitution starts a game. It must be
+// called during startup wiring, before the reaper runs; the default is
+// notify.Nop (no live events; waiters still discover the game via Poll).
+func (m *Matchmaker) SetNotifier(p notify.Publisher) {
+	if p != nil {
+		m.pub = p
+	}
+}
+
+// emitMatchFound pushes match_found to every seat of a freshly started game.
+// Emitting to a robot seat is harmless (no client subscription exists for it).
+func (m *Matchmaker) emitMatchFound(g game.Game) {
+	intents := make([]notify.Intent, 0, len(g.Seats))
+	for _, s := range g.Seats {
+		intents = append(intents, notify.MatchFound(s.AccountID, g.ID))
+	}
+	m.pub.Publish(intents...)
+}
+
 // EnqueueResult reports the outcome of joining the pool: either a started game or a
 // queued ticket awaiting an opponent.
 type EnqueueResult struct {
@@ -102,6 +125,7 @@ func (m *Matchmaker) Enqueue(ctx context.Context, accountID uuid.UUID, variant e
 	m.mu.Lock()
 	m.results[opponent] = g
 	m.mu.Unlock()
+	m.emitMatchFound(g)
 	return EnqueueResult{Matched: true, Game: g}, nil
 }
 
@@ -197,6 +221,7 @@ func (m *Matchmaker) Reap(ctx context.Context, now time.Time) {
 		m.mu.Lock()
 		m.results[s.human] = g
 		m.mu.Unlock()
+		m.emitMatchFound(g)
 	}
 }