feat(chat): unread read-receipts with lobby/game dot and history-open ack

Persist per-message read state as a chat_messages.unread_seats bitmask
(migration 00008): a text message seeds every recipient seat's bit, a nudge
only the awaited seat's. A seat's bit clears when the player opens the move
history or chat (POST /games/:id/chat/read, sent only when something is
unread), and a nudge additionally clears when its recipient answers by moving
(a wired game NudgeClearer, dependency-inverted so game keeps off social).

UI shows a per-viewer unread dot in the lobby (next to the opponent) and the
game score bar — the unread_chat game-view flag seeds it from authoritative
REST views, live chat/nudge events raise it. Opening the move history counts
as reading (even without entering chat): the 💬 fade-blinks twice and the
client acks. Admin Messages gains an unread-only filter, a read/unread column,
and a per-message card with the per-seat read breakdown. Observability:
chat_read_duration histogram + chat_unread_messages gauge + social tracing.

gateway/internal/transcode/transcode.go

@@ -40,6 +40,7 @@ const (
 	MsgGameHistory    = "game.history"
 	MsgChatList       = "chat.list"
 	MsgChatNudge      = "chat.nudge"
+	MsgChatRead       = "chat.read"
 	MsgDraftGet       = "draft.get"
 	MsgDraftSave      = "draft.save"
 	MsgGameHide       = "game.hide"
@@ -121,6 +122,7 @@ func NewRegistry(backend *backendclient.Client, tg TelegramValidator, defaultLan
 	r.ops[MsgGameHistory] = Op{Handler: historyHandler(backend), Auth: true}
 	r.ops[MsgChatList] = Op{Handler: chatListHandler(backend), Auth: true}
 	r.ops[MsgChatNudge] = Op{Handler: nudgeHandler(backend), Auth: true}
+	r.ops[MsgChatRead] = Op{Handler: markChatReadHandler(backend), Auth: true}
 	r.ops[MsgDraftGet] = Op{Handler: getDraftHandler(backend), Auth: true}
 	r.ops[MsgDraftSave] = Op{Handler: saveDraftHandler(backend), Auth: true}
 	r.ops[MsgGameHide] = Op{Handler: hideGameHandler(backend), Auth: true}
@@ -451,6 +453,18 @@ func nudgeHandler(backend *backendclient.Client) Handler {
 	}
 }
 
+// markChatReadHandler acknowledges the caller has read the game's chat. It reuses
+// GameActionRequest for the game id and echoes an Ack.
+func markChatReadHandler(backend *backendclient.Client) Handler {
+	return func(ctx context.Context, req Request) ([]byte, error) {
+		in := fb.GetRootAsGameActionRequest(req.Payload, 0)
+		if err := backend.MarkChatRead(ctx, req.UserID, string(in.GameId())); err != nil {
+			return nil, err
+		}
+		return encodeAck(true), nil
+	}
+}
+
 // getDraftHandler returns the player's saved composition. It reuses
 // GameActionRequest for the game id and wraps the backend's raw JSON in a DraftView.
 func getDraftHandler(backend *backendclient.Client) Handler {