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/internal/social/chat.go

@@ -100,7 +100,7 @@ func (svc *Service) PostMessage(ctx context.Context, gameID, senderID uuid.UUID,
 	if err := Clean(body); err != nil {
 		return Message{}, err
 	}
-	msg, err := svc.store.insertChatMessage(ctx, gameID, senderID, kindMessage, body, parseIP(senderIP))
+	msg, err := svc.store.insertChatMessage(ctx, gameID, senderID, kindMessage, body, parseIP(senderIP), recipientMask(seats, senderID))
 	if err != nil {
 		return Message{}, err
 	}
@@ -148,7 +148,7 @@ func (svc *Service) Nudge(ctx context.Context, gameID, senderID uuid.UUID) (Mess
 			return Message{}, ErrNudgeTooSoon
 		}
 	}
-	msg, err := svc.store.insertChatMessage(ctx, gameID, senderID, kindNudge, "", nil)
+	msg, err := svc.store.insertChatMessage(ctx, gameID, senderID, kindNudge, "", nil, int16(1)<<uint(toMove))
 	if err != nil {
 		return Message{}, err
 	}
@@ -258,8 +258,22 @@ func parseIP(raw string) *string {
 	return &canon
 }
 
-// insertChatMessage stores one chat row and returns it.
-func (s *Store) insertChatMessage(ctx context.Context, gameID, senderID uuid.UUID, kind, body string, ip *string) (Message, error) {
+// recipientMask is the initial unread bitmask for a text message: a set bit for every
+// seated recipient (by seat index) other than the sender. Still-empty (open) seats are
+// skipped. With at most four seats the result always fits the smallint column.
+func recipientMask(seats []uuid.UUID, senderID uuid.UUID) int16 {
+	var mask int16
+	for i, id := range seats {
+		if id == uuid.Nil || id == senderID {
+			continue
+		}
+		mask |= int16(1) << uint(i)
+	}
+	return mask
+}
+
+// insertChatMessage stores one chat row, seeding its unread bitmask, and returns it.
+func (s *Store) insertChatMessage(ctx context.Context, gameID, senderID uuid.UUID, kind, body string, ip *string, unreadMask int16) (Message, error) {
 	id, err := uuid.NewV7()
 	if err != nil {
 		return Message{}, fmt.Errorf("social: new message id: %w", err)
@@ -271,7 +285,8 @@ func (s *Store) insertChatMessage(ctx context.Context, gameID, senderID uuid.UUI
 	stmt := table.ChatMessages.INSERT(
 		table.ChatMessages.MessageID, table.ChatMessages.GameID, table.ChatMessages.SenderID,
 		table.ChatMessages.Kind, table.ChatMessages.Body, table.ChatMessages.SenderIP,
-	).VALUES(id, gameID, senderID, kind, body, ipVal).
+		table.ChatMessages.UnreadSeats,
+	).VALUES(id, gameID, senderID, kind, body, ipVal, unreadMask).
 		RETURNING(table.ChatMessages.AllColumns)
 	var row model.ChatMessages
 	if err := stmt.QueryContext(ctx, s.db, &row); err != nil {