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.

pkg/fbs/scrabble.fbs

@@ -73,6 +73,9 @@ table GameView {
   // vs_ai marks an honest-AI game: the opponent is shown as 🤖 and chat/nudge/add-friend
   // are disabled in the client. A robot-filled random game keeps vs_ai=false.
   vs_ai:bool;
+  // unread_chat is a per-viewer flag: the requesting player has at least one unread chat
+  // entry (message or nudge) in this game. It drives the lobby and in-game unread badge.
+  unread_chat:bool;
 }
 
 // MoveRecord is one decoded move (a committed play, or a hint preview).

pkg/fbs/scrabblefb/GameView.go

@@ -185,8 +185,20 @@ func (rcv *GameView) MutateVsAi(n bool) bool {
 	return rcv._tab.MutateBoolSlot(28, n)
 }
 
+func (rcv *GameView) UnreadChat() bool {
+	o := flatbuffers.UOffsetT(rcv._tab.Offset(30))
+	if o != 0 {
+		return rcv._tab.GetBool(o + rcv._tab.Pos)
+	}
+	return false
+}
+
+func (rcv *GameView) MutateUnreadChat(n bool) bool {
+	return rcv._tab.MutateBoolSlot(30, n)
+}
+
 func GameViewStart(builder *flatbuffers.Builder) {
-	builder.StartObject(13)
+	builder.StartObject(14)
 }
 func GameViewAddId(builder *flatbuffers.Builder, id flatbuffers.UOffsetT) {
 	builder.PrependUOffsetTSlot(0, flatbuffers.UOffsetT(id), 0)
@@ -230,6 +242,9 @@ func GameViewAddLastActivityUnix(builder *flatbuffers.Builder, lastActivityUnix
 func GameViewAddVsAi(builder *flatbuffers.Builder, vsAi bool) {
 	builder.PrependBoolSlot(12, vsAi, false)
 }
+func GameViewAddUnreadChat(builder *flatbuffers.Builder, unreadChat bool) {
+	builder.PrependBoolSlot(13, unreadChat, false)
+}
 func GameViewEnd(builder *flatbuffers.Builder) flatbuffers.UOffsetT {
 	return builder.EndObject()
 }