UI: fix the lobby slide on Telegram cold launch (correct the cause)

The first attempt (the App.svelte `started` gate) targeted the first pane mount,
but the slide is a second render. On a Telegram cold launch the URL fragment is
Telegram's #tgWebAppData=... launch params, which the router parsed as notfound;
bootstrap's navigate('/') then corrected it to the lobby asynchronously, re-keying
the route pane (notfound -> lobby) and sliding the lobby in as if returning from a
screen. A reload was static because the hash was already #/.

Treat a Telegram launch fragment as the lobby root in the router, so the route is
correct from the first pane (no re-key, no slide). Extract the pure hash->Route
parsing into routeparse.ts so it unit-tests without a DOM, and revert the gate
(the first pane never slid — local transitions skip the initial mount, as clean
browser launches showed).

Tests: routeparse unit tests (incl. the tgWebApp fragment); an e2e that launches
with the fragment in the URL and asserts the lobby plus the normalised #/ hash.

ui/src/lib/router.svelte.ts

@@ -1,54 +1,11 @@
 // Minimal dependency-free hash router. Hash routing survives a reload and works on
 // a file:// origin (Capacitor native packaging), where there is no server to honour
-// deep paths. The route is a reactive rune so screens re-render on navigation.
+// deep paths. The route is a reactive rune so screens re-render on navigation. The pure
+// hash->Route parsing lives in routeparse.ts (unit-tested without a DOM).
 
-export type RouteName =
-  | 'login'
-  | 'lobby'
-  | 'new'
-  | 'game'
-  | 'gameChat'
-  | 'gameCheck'
-  | 'profile'
-  | 'settings'
-  | 'about'
-  | 'friends'
-  | 'stats'
-  | 'notfound';
+import { parse, type Route, type RouteName } from './routeparse';
 
-export interface Route {
-  name: RouteName;
-  params: Record<string, string>;
-}
-
-function parse(hash: string): Route {
-  const path = (hash.replace(/^#/, '') || '/').split('?')[0];
-  const seg = path.split('/').filter(Boolean);
-  if (seg.length === 0) return { name: 'lobby', params: {} };
-  switch (seg[0]) {
-    case 'login':
-      return { name: 'login', params: {} };
-    case 'new':
-      return { name: 'new', params: {} };
-    case 'game':
-      if (!seg[1]) return { name: 'notfound', params: {} };
-      if (seg[2] === 'chat') return { name: 'gameChat', params: { id: seg[1] } };
-      if (seg[2] === 'check') return { name: 'gameCheck', params: { id: seg[1] } };
-      return { name: 'game', params: { id: seg[1] } };
-    case 'profile':
-      return { name: 'profile', params: {} };
-    case 'settings':
-      return { name: 'settings', params: {} };
-    case 'about':
-      return { name: 'about', params: {} };
-    case 'friends':
-      return { name: 'friends', params: {} };
-    case 'stats':
-      return { name: 'stats', params: {} };
-    default:
-      return { name: 'notfound', params: {} };
-  }
-}
+export type { Route, RouteName };
 
 export const router = $state<{ route: Route }>({
   route: parse(typeof location !== 'undefined' ? location.hash : ''),