feat(rooms): real server-side private games with friend invites (no bot swap)

Private rooms were 100% client-simulated (the "friend" auto-accepted then bots
filled invited seats). Now they're server-authoritative over SignalR:

Server (GameManager.PrivateRooms + GameHub):
- Room registry with create/invite/accept/decline/addBot/clearSeat/start/leave.
- Invite pushes a `roomInvite` to that user (Clients.User); the seat stays
  "invited" (a pending guest with their real profile, resolved server-side) — it
  is NEVER replaced by a bot.
- StartPrivate refuses while any invite is pending; only EMPTY seats fill with
  bots. Then it spins up a live GameRoom and matchFound → both devices enter.
- Host leave / disconnect closes the room (roomClosed); members free their seat.

Client:
- signalr-service implements the room methods over the hub (+ room/roomInvite/
  roomClosed events, room mapping, onRoomInvite); mock keeps offline no-ops.
- online-store accept/declineInvite; RoomScreen blocks "Start" while an invite
  is pending and auto-enters the live game on matchFound (host + friend).
- New global InviteModal (accept/decline) + i18n (invite.*, room.waitAccept).

Addresses: (1) no bot replacement, (2) game waits for acceptance, (3) invited
friend shown as a pending guest with their name/avatar.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/app/page.tsx

@@ -22,6 +22,7 @@ import { ResumeGameBar } from "@/components/online/ResumeGameBar";
 import { CelebrationOverlay } from "@/components/online/CelebrationOverlay";
 import { ErrorBoundary } from "@/components/ErrorBoundary";
 import { PublicProfileModal } from "@/components/online/PublicProfileModal";
+import { InviteModal } from "@/components/online/InviteModal";
 import { CapacitorBack } from "@/components/CapacitorBack";
 import { useSessionStore } from "@/lib/session-store";
 import { useGameStore } from "@/lib/game-store";
@@ -209,6 +210,7 @@ export default function Page() {
         <ResumeGameBar />
         <CelebrationOverlay />
         <PublicProfileModal />
+        <InviteModal />
       </ErrorBoundary>
       <CapacitorBack />
       {loading && null}