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.

ui/src/gen/fbs/scrabblefb/game-view.ts

@@ -103,8 +103,13 @@ vsAi():boolean {
   return offset ? !!this.bb!.readInt8(this.bb_pos + offset) : false;
 }
 
+unreadChat():boolean {
+  const offset = this.bb!.__offset(this.bb_pos, 30);
+  return offset ? !!this.bb!.readInt8(this.bb_pos + offset) : false;
+}
+
 static startGameView(builder:flatbuffers.Builder) {
-  builder.startObject(13);
+  builder.startObject(14);
 }
 
 static addId(builder:flatbuffers.Builder, idOffset:flatbuffers.Offset) {
@@ -171,12 +176,16 @@ static addVsAi(builder:flatbuffers.Builder, vsAi:boolean) {
   builder.addFieldInt8(12, +vsAi, +false);
 }
 
+static addUnreadChat(builder:flatbuffers.Builder, unreadChat:boolean) {
+  builder.addFieldInt8(13, +unreadChat, +false);
+}
+
 static endGameView(builder:flatbuffers.Builder):flatbuffers.Offset {
   const offset = builder.endObject();
   return offset;
 }
 
-static createGameView(builder:flatbuffers.Builder, idOffset:flatbuffers.Offset, variantOffset:flatbuffers.Offset, dictVersionOffset:flatbuffers.Offset, statusOffset:flatbuffers.Offset, players:number, toMove:number, turnTimeoutSecs:number, multipleWordsPerTurn:boolean, moveCount:number, endReasonOffset:flatbuffers.Offset, seatsOffset:flatbuffers.Offset, lastActivityUnix:bigint, vsAi:boolean):flatbuffers.Offset {
+static createGameView(builder:flatbuffers.Builder, idOffset:flatbuffers.Offset, variantOffset:flatbuffers.Offset, dictVersionOffset:flatbuffers.Offset, statusOffset:flatbuffers.Offset, players:number, toMove:number, turnTimeoutSecs:number, multipleWordsPerTurn:boolean, moveCount:number, endReasonOffset:flatbuffers.Offset, seatsOffset:flatbuffers.Offset, lastActivityUnix:bigint, vsAi:boolean, unreadChat:boolean):flatbuffers.Offset {
   GameView.startGameView(builder);
   GameView.addId(builder, idOffset);
   GameView.addVariant(builder, variantOffset);
@@ -191,6 +200,7 @@ static createGameView(builder:flatbuffers.Builder, idOffset:flatbuffers.Offset,
   GameView.addSeats(builder, seatsOffset);
   GameView.addLastActivityUnix(builder, lastActivityUnix);
   GameView.addVsAi(builder, vsAi);
+  GameView.addUnreadChat(builder, unreadChat);
   return GameView.endGameView(builder);
 }
 }