fix: sent messages not appearing + add Lobby/Auth skeleton loaders

- Fix timelineSegments useMemo stale cache: the Perf-5 optimization used
  timeline.linkedTimelines as its only dep, but that reference never changes
  when events are added in-place; adding eventsLength as a dep makes it
  recompute on every new live event so the binary search always finds the
  new item
- Add LobbySkeleton: shimmer placeholder for space lobby (header + hero +
  room list rows) shown while the Lobby chunk lazy-loads
- Add AuthSkeleton: shimmer placeholder for auth pages (logo + server
  picker + form fields) shown while AuthLayout chunk lazy-loads
- Wire both into Router.tsx fallback props

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

src/app/pages/Router.tsx

@@ -8,6 +8,8 @@ import {
   redirect,
 } from 'react-router-dom';
 import { RoomSkeleton } from '../components/RoomSkeleton';
+import { LobbySkeleton } from '../components/LobbySkeleton';
+import { AuthSkeleton } from '../components/AuthSkeleton';
 
 import { ClientConfig } from '../hooks/useClientConfig';
 import {
@@ -124,7 +126,7 @@ export const createRouter = (clientConfig: ClientConfig, screenSize: ScreenSize)
           return null;
         }}
         element={
-          <React.Suspense fallback={null}>
+          <React.Suspense fallback={<AuthSkeleton />}>
             <AuthLayout />
             <UnAuthRouteThemeManager />
           </React.Suspense>
@@ -309,7 +311,7 @@ export const createRouter = (clientConfig: ClientConfig, screenSize: ScreenSize)
           <Route
             path={_LOBBY_PATH}
             element={
-              <React.Suspense fallback={null}>
+              <React.Suspense fallback={<LobbySkeleton />}>
                 <Lobby />
               </React.Suspense>
             }