feat(demo): typing splash + intro on every fresh visit; neutral desktop Cloud tabs

- Demo boots at '/' (first visit or a browser refresh) always start with
  the typing splash into the onboarding intro — the per-calendar-day
  gate is gone. In-session SPA navigation never replays it, and
  deep-route refreshes keep the visitor's place.
- Cloud top-level tabs return to the standard mode-switcher style on
  desktop; the orange full-width switcher stays mobile-only.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

neode-ui/src/App.vue

@@ -398,8 +398,13 @@ onMounted(async () => {
   // One-shot "Replay intro" request from the login screen — must survive the
   // auto-re-mark below (which otherwise instantly suppresses the replay on any
   // onboarded node).
-  const replayRequested = sessionStorage.getItem('archipelago_replay_intro') === '1'
+  let replayRequested = sessionStorage.getItem('archipelago_replay_intro') === '1'
   if (replayRequested) sessionStorage.removeItem('archipelago_replay_intro')
+  // Public demo: every fresh boot at the root (first visit or a browser
+  // refresh) starts with the typing splash for the full effect. In-session SPA
+  // navigation never remounts App, and deep-route refreshes keep their place.
+  const { IS_DEMO } = await import('@/composables/useDemoIntro')
+  if (IS_DEMO && route.path === '/') replayRequested = true
   let onboardingComplete: boolean | null = localStorage.getItem('neode_onboarding_complete') === '1' ? true : null
   const splashCandidate = !seenIntro
     && (fromBoot || (route.path === '/' && import.meta.env.VITE_DEV_MODE !== 'boot'))