feat(lobby): keep lobby/game caches fresh from any screen + invitation delta channel

Builds on the cross-screen cache work: the global stream handler now keeps both
caches current no matter which screen is mounted, and invitations become a live
delta channel so the lobby's invitations list is fresh from any screen too.

Client (boundary already started):
- advanceCached now also folds opponent_joined into a not-currently-viewed game's
  cache via a new pure reducer applyOpponentJoined (extracted and reused by the
  mounted game board), so opening an open game that filled while you were elsewhere
  is flash-free.
- patchLobbyInvitation upserts a still-pending invitation and removes a terminal
  one (started/declined/cancelled/expired); the global notify handler calls it on
  the invitation / invitation_update sub-kinds.

Invitations delta channel (no wire/gateway/connector change — the notification
already carries the full invitation with id/status/game_id end to end):
- notify: a new in-app-only NotifyInvitationUpdate sub + NotificationInvitationUpdate
  constructor (shares encoding with NotificationInvitation). The Telegram connector
  renders no message for it, so a decline/cancel never becomes an out-of-app push.
- lobby: emit the changed invitation to every participant on respond (accept/decline),
  on the final accept's game start, and on cancel — so each participant's lobby patches
  its list in place. The authoritative list holds only pending invitations, so the
  client's pending-vs-terminal rule matches it exactly.

Tests: applyOpponentJoined + patchLobbyInvitation unit tests (TDD), the
NotificationInvitationUpdate encoding unit test, and integration assertions that
decline/cancel/accept publish invitation_update to every participant. Full local
suite green (backend unit+integration, UI check/unit/build/bundle/e2e). Docs:
ARCHITECTURE §10 (notify catalog + in-app-only note) and UI_DESIGN updated.

backend/internal/inttest/lobby_test.go

@@ -13,6 +13,7 @@ import (
 	"scrabble/backend/internal/account"
 	"scrabble/backend/internal/engine"
 	"scrabble/backend/internal/lobby"
+	"scrabble/backend/internal/notify"
 )
 
 // newInvitationService builds an invitation service over the shared pool, starting
@@ -97,6 +98,8 @@ func TestMatchmakingReEnqueueReturnsOwnOpenGame(t *testing.T) {
 func TestInvitationAllAcceptStartsGame(t *testing.T) {
 	ctx := context.Background()
 	svc := newInvitationService()
+	pub := &capturePublisher{}
+	svc.SetNotifier(pub)
 	inviter := provisionAccount(t)
 	invitees := []uuid.UUID{provisionAccount(t), provisionAccount(t)}
 
@@ -118,6 +121,16 @@ func TestInvitationAllAcceptStartsGame(t *testing.T) {
 	if final.Status != "started" || final.GameID == nil {
 		t.Fatalf("invitation not started: %+v", final)
 	}
+	// Every participant is told the invitation changed so their lobby drops the (now started) card
+	// from any screen, and the started-game notification lands too.
+	for _, u := range append([]uuid.UUID{inviter}, invitees...) {
+		if !pub.notified(u, notify.NotifyInvitationUpdate) {
+			t.Errorf("participant %s missing invitation_update", u)
+		}
+	}
+	if !pub.notified(invitees[0], notify.NotifyGameStarted) {
+		t.Errorf("invitee missing game_started")
+	}
 	seats, _, status, err := newGameService().Participants(ctx, *final.GameID)
 	if err != nil {
 		t.Fatalf("participants: %v", err)
@@ -130,6 +143,8 @@ func TestInvitationAllAcceptStartsGame(t *testing.T) {
 func TestInvitationDeclineCancels(t *testing.T) {
 	ctx := context.Background()
 	svc := newInvitationService()
+	pub := &capturePublisher{}
+	svc.SetNotifier(pub)
 	inviter := provisionAccount(t)
 	invitees := []uuid.UUID{provisionAccount(t), provisionAccount(t)}
 	inv, err := svc.CreateInvitation(ctx, inviter, invitees, englishInvite())
@@ -143,6 +158,12 @@ func TestInvitationDeclineCancels(t *testing.T) {
 	if got.Status != "declined" || got.GameID != nil {
 		t.Fatalf("after decline: %+v", got)
 	}
+	// A decline kills the whole invitation: every participant is notified to drop it.
+	for _, u := range append([]uuid.UUID{inviter}, invitees...) {
+		if !pub.notified(u, notify.NotifyInvitationUpdate) {
+			t.Errorf("participant %s missing invitation_update after decline", u)
+		}
+	}
 	// A further response is refused.
 	if _, err := svc.RespondInvitation(ctx, inv.ID, invitees[1], true); !errors.Is(err, lobby.ErrInvitationNotPending) {
 		t.Fatalf("respond after decline = %v, want ErrInvitationNotPending", err)
@@ -184,6 +205,8 @@ func TestInvitationBlockedInvitee(t *testing.T) {
 func TestInvitationCancelByInviter(t *testing.T) {
 	ctx := context.Background()
 	svc := newInvitationService()
+	pub := &capturePublisher{}
+	svc.SetNotifier(pub)
 	inviter := provisionAccount(t)
 	invitees := []uuid.UUID{provisionAccount(t)}
 	inv, err := svc.CreateInvitation(ctx, inviter, invitees, englishInvite())
@@ -197,6 +220,12 @@ func TestInvitationCancelByInviter(t *testing.T) {
 	if err := svc.CancelInvitation(ctx, inv.ID, inviter); err != nil {
 		t.Fatalf("inviter cancel: %v", err)
 	}
+	// The cancellation reaches every participant so an invitee's lobby drops the card from any screen.
+	for _, u := range append([]uuid.UUID{inviter}, invitees...) {
+		if !pub.notified(u, notify.NotifyInvitationUpdate) {
+			t.Errorf("participant %s missing invitation_update after cancel", u)
+		}
+	}
 	if _, err := svc.RespondInvitation(ctx, inv.ID, invitees[0], true); !errors.Is(err, lobby.ErrInvitationNotPending) {
 		t.Fatalf("respond after cancel = %v, want ErrInvitationNotPending", err)
 	}