feat: add landing page components including hero, features, problem, and footer

- Introduced LandingHero component with logo, tagline, and action buttons.
- Created LandingFeatures component to showcase chore system benefits.
- Developed LandingProblem component explaining the importance of a structured chore system.
- Implemented LandingFooter for navigation and copyright information.
- Added LandingPage to assemble all components and manage navigation.
- Included unit tests for LandingHero component to ensure functionality.

frontend/vue-app/src/stores/auth.ts

@@ -134,8 +134,8 @@ export function initAuthSync() {
       const payload = JSON.parse(event.newValue)
       if (payload?.type === 'logout') {
         applyLoggedOutState()
-        if (!window.location.pathname.startsWith('/auth')) {
-          window.location.href = '/auth/login'
+        if (!window.location.pathname.startsWith('/auth') && window.location.pathname !== '/') {
+          window.location.href = '/'
         }
       } else if (payload?.type === 'parent_logout') {
         applyParentLoggedOutState()