Stage 17 round 6 (#10 backend): enforce chat only on your turn

PostMessage now rejects a chat sent on a finished game or when it is not the sender's
turn (ErrChatNotYourTurn -> 409 chat_not_your_turn), matching the UI where the message
field is hidden off-turn and only the nudge shows. Existing chat tests post on the
to-move seat and are unaffected; adds an off-turn-rejection integration test + the dto
mapping case + the UI error message.

backend/internal/inttest/social_test.go

@@ -314,6 +314,20 @@ func TestChatRejectsBadContent(t *testing.T) {
 	}
 }
 
+// TestChatOnlyOnYourTurn checks chat is allowed only on the sender's own turn (Stage 17):
+// the player to move can post, the waiting player gets ErrChatNotYourTurn.
+func TestChatOnlyOnYourTurn(t *testing.T) {
+	ctx := context.Background()
+	svc := newSocialService()
+	gameID, seats := newGameWithSeats(t, 2) // seat 0 is to move at the opening
+	if _, err := svc.PostMessage(ctx, gameID, seats[1], "hi", ""); !errors.Is(err, social.ErrChatNotYourTurn) {
+		t.Fatalf("off-turn chat = %v, want ErrChatNotYourTurn", err)
+	}
+	if _, err := svc.PostMessage(ctx, gameID, seats[0], "hi", ""); err != nil {
+		t.Fatalf("on-turn chat = %v, want nil", err)
+	}
+}
+
 func TestNudgeRulesAndRateLimit(t *testing.T) {
 	ctx := context.Background()
 	svc := newSocialService()