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/wire/build.go

@@ -44,6 +44,8 @@ type GameView struct {
 	LastActivityUnix     int64
 	// VsAI marks an honest-AI game (the opponent is shown as 🤖, chat/nudge/add-friend off).
 	VsAI bool
+	// UnreadChat is a per-viewer flag: the requesting player has unread chat in this game.
+	UnreadChat bool
 }
 
 // TileRecord is one tile in a decoded MoveRecord (the concrete letter, "?" for a blank
@@ -161,6 +163,7 @@ func BuildGameView(b *flatbuffers.Builder, g GameView) flatbuffers.UOffsetT {
 	fb.GameViewAddSeats(b, seats)
 	fb.GameViewAddLastActivityUnix(b, g.LastActivityUnix)
 	fb.GameViewAddVsAi(b, g.VsAI)
+	fb.GameViewAddUnreadChat(b, g.UnreadChat)
 	return fb.GameViewEnd(b)
 }