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.

backend/cmd/backend/main.go

@@ -169,6 +169,8 @@ func run(ctx context.Context, cfg config.Config, logger *zap.Logger) error {
 	socialSvc := social.NewService(social.NewStore(db), accounts, games)
 	socialSvc.SetNotifier(hub)
 	socialSvc.SetMetrics(tel.MeterProvider().Meter("scrabble/backend/social"))
+	// A nudge the recipient answered by moving is marked read on the move path.
+	games.SetNudgeClearer(socialSvc.ClearNudges)
 	feedbackSvc := feedback.NewService(feedback.NewStore(db), accounts)
 	feedbackSvc.SetNotifier(hub)