Refactor AppHeader and AreaTabs components for improved layout and functionality

- Adjusted AppHeader.vue for better spacing and alignment of elements, enhancing the overall visual appeal.
- Updated AreaTabs.vue to include a new 'Start' tab with a home icon, improving navigation options.
- Modified route handling in AreaTabs.vue to dynamically determine the current area based on the route.
- Changed default redirect destination in useAuth.ts to the root path for a more intuitive user experience.
- Enhanced index.vue to provide a more welcoming message and improved content presentation.

These changes aim to enhance user navigation and overall experience within the application.

app/pages/index.vue

@@ -11,18 +11,18 @@ const handleClick = () => {
 <template>
   <NuxtLayout name="default">
     <div class="max-w-7xl mx-auto px-4 sm:px-6 lg:px-8 py-12">
-      <!-- Welcome Section -->
-      <div class="mb-8">
-        <h1 class="text-4xl font-bold mb-4">
+      <!-- Page Header -->
+      <div class="mx-auto mb-12 max-w-container-wide text-center">
+        <h1 class="mb-4 text-4xl font-bold text-white md:text-5xl">
           <template v-if="loggedIn">
             Willkommen zurück, {{ user?.firstName }}!
           </template>
           <template v-else>
-            Welcome to my.experimenta
+            Willkommen!
           </template>
         </h1>
-        <p class="text-lg text-white/90">
-          Your gateway to Makerspace annual passes and more.
+        <p class="mx-auto max-w-2xl text-lg text-white/80">
+          Entdecke die vielfältigen Angebote der experimenta - wir freuen uns auf dich!
         </p>
       </div>
 
@@ -44,8 +44,8 @@ const handleClick = () => {
       <div class="card-info card-accent-border mb-8">
         <h2 class="text-xl font-semibold mb-2 text-experimenta-accent">MVP Development in Progress</h2>
         <p>
-          This is a placeholder page. The full e-commerce functionality will be implemented in
-          upcoming phases.
+          Dies ist eine Platzhalter-Seite. Die vollständige E-Commerce-Funktionalität wird in
+          kommenden Phasen implementiert.
         </p>
       </div>