Stage 17 round 6 (#7): reset the nudge cooldown once the player acts

The hourly nudge cooldown now clears as soon as the sender has moved or posted a chat
since their last nudge — engagement lifts the 'don't spam' limit. Backend: Nudge checks
game.LastMoveAt + the sender's last non-nudge chat against the last nudge time
(GameReader gains LastMoveAt). UI: nudgeOnCooldown mirrors it — a chat reset is read from
the message list, a move is tracked client-side (lastActedAt on commit/pass/exchange; the
backend stays authoritative across a reload). Integration test covers the reset.

backend/internal/social/chat.go

@@ -114,7 +114,15 @@ func (svc *Service) Nudge(ctx context.Context, gameID, senderID uuid.UUID) (Mess
 		return Message{}, err
 	}
 	if ok && svc.now().Sub(last) < nudgeInterval {
-		return Message{}, ErrNudgeTooSoon
+		// The cooldown resets once the sender has acted (moved or chatted) since the last
+		// nudge — engagement clears the "don't spam" limit (Stage 17).
+		acted, err := svc.actedSince(ctx, gameID, senderID, last)
+		if err != nil {
+			return Message{}, err
+		}
+		if !acted {
+			return Message{}, ErrNudgeTooSoon
+		}
 	}
 	msg, err := svc.store.insertChatMessage(ctx, gameID, senderID, kindNudge, "", nil)
 	if err != nil {
@@ -127,6 +135,22 @@ func (svc *Service) Nudge(ctx context.Context, gameID, senderID uuid.UUID) (Mess
 	return msg, nil
 }
 
+// actedSince reports whether senderID made a move or posted a chat message in the game
+// after t — the events that reset the nudge cooldown (Stage 17).
+func (svc *Service) actedSince(ctx context.Context, gameID, senderID uuid.UUID, t time.Time) (bool, error) {
+	if mv, ok, err := svc.games.LastMoveAt(ctx, gameID, senderID); err != nil {
+		return false, err
+	} else if ok && mv.After(t) {
+		return true, nil
+	}
+	if msg, ok, err := svc.store.lastMessageAt(ctx, gameID, senderID); err != nil {
+		return false, err
+	} else if ok && msg.After(t) {
+		return true, nil
+	}
+	return false, nil
+}
+
 // emitChat pushes a chat message to every seated player except the sender
 // (best-effort live delivery; the recipients still read it via Messages).
 func (svc *Service) emitChat(seats []uuid.UUID, senderID uuid.UUID, m Message) {
@@ -261,6 +285,27 @@ func (s *Store) lastNudgeAt(ctx context.Context, gameID, senderID uuid.UUID) (ti
 	return row.CreatedAt, true, nil
 }
 
+// lastMessageAt returns the time of senderID's most recent non-nudge chat message in
+// gameID, if any. The nudge cooldown resets when the player chats (or moves), so a stale
+// nudge no longer blocks a new one (Stage 17).
+func (s *Store) lastMessageAt(ctx context.Context, gameID, senderID uuid.UUID) (time.Time, bool, error) {
+	stmt := postgres.SELECT(table.ChatMessages.CreatedAt).
+		FROM(table.ChatMessages).
+		WHERE(
+			table.ChatMessages.GameID.EQ(postgres.UUID(gameID)).
+				AND(table.ChatMessages.SenderID.EQ(postgres.UUID(senderID))).
+				AND(table.ChatMessages.Kind.EQ(postgres.String(kindMessage))),
+		).ORDER_BY(table.ChatMessages.CreatedAt.DESC()).LIMIT(1)
+	var row model.ChatMessages
+	if err := stmt.QueryContext(ctx, s.db, &row); err != nil {
+		if errors.Is(err, qrm.ErrNoRows) {
+			return time.Time{}, false, nil
+		}
+		return time.Time{}, false, fmt.Errorf("social: last message: %w", err)
+	}
+	return row.CreatedAt, true, nil
+}
+
 // messageFromRow projects a generated row into the public Message.
 func messageFromRow(r model.ChatMessages) Message {
 	m := Message{

backend/internal/social/social.go

@@ -28,6 +28,9 @@ type GameReader interface {
 	// SharedGame reports whether two accounts are seated together in any game
 	// (active or finished); it gates the "befriend an opponent" request path.
 	SharedGame(ctx context.Context, a, b uuid.UUID) (bool, error)
+	// LastMoveAt is the time of an account's most recent move in a game (and whether it
+	// has moved); the nudge cooldown resets once the player has taken a turn.
+	LastMoveAt(ctx context.Context, gameID, accountID uuid.UUID) (time.Time, bool, error)
 }
 
 // Sentinel errors returned by the service.