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/social/chat.go

@@ -14,6 +14,7 @@ import (
 	"github.com/go-jet/jet/v2/qrm"
 	"github.com/google/uuid"
 
+	"scrabble/backend/internal/notify"
 	"scrabble/backend/internal/postgres/jet/backend/model"
 	"scrabble/backend/internal/postgres/jet/backend/table"
 )
@@ -72,7 +73,12 @@ func (svc *Service) PostMessage(ctx context.Context, gameID, senderID uuid.UUID,
 	if err := Clean(body); err != nil {
 		return Message{}, err
 	}
-	return svc.store.insertChatMessage(ctx, gameID, senderID, kindMessage, body, parseIP(senderIP))
+	msg, err := svc.store.insertChatMessage(ctx, gameID, senderID, kindMessage, body, parseIP(senderIP))
+	if err != nil {
+		return Message{}, err
+	}
+	svc.emitChat(seats, senderID, msg)
+	return msg, nil
 }
 
 // Nudge records a nudge from senderID toward the player whose turn is awaited. The
@@ -100,7 +106,27 @@ func (svc *Service) Nudge(ctx context.Context, gameID, senderID uuid.UUID) (Mess
 	if ok && svc.now().Sub(last) < nudgeInterval {
 		return Message{}, ErrNudgeTooSoon
 	}
-	return svc.store.insertChatMessage(ctx, gameID, senderID, kindNudge, "", nil)
+	msg, err := svc.store.insertChatMessage(ctx, gameID, senderID, kindNudge, "", nil)
+	if err != nil {
+		return Message{}, err
+	}
+	if toMove >= 0 && toMove < len(seats) {
+		svc.pub.Publish(notify.Nudge(seats[toMove], gameID, senderID))
+	}
+	return msg, nil
+}
+
+// emitChat pushes a chat message to every seated player except the sender
+// (best-effort live delivery; the recipients still read it via Messages).
+func (svc *Service) emitChat(seats []uuid.UUID, senderID uuid.UUID, m Message) {
+	intents := make([]notify.Intent, 0, len(seats))
+	for _, id := range seats {
+		if id == senderID {
+			continue
+		}
+		intents = append(intents, notify.ChatMessage(id, m.GameID, m.SenderID, m.ID.String(), m.Kind, m.Body, m.CreatedAt))
+	}
+	svc.pub.Publish(intents...)
 }
 
 // LastNudgeAt returns the time of the most recent nudge senderID sent in the game