refactor: Simplify logout process and enhance routing in authentication components

- Remove unnecessary async handling in logout functions across UserProfile.vue and Navbar.vue.
- Integrate `useRouter` for consistent redirection to the login page after logout.
- Update `logout` method in useAuth.ts to clear local state without an API call.

src/components/layout/Navbar.vue

@@ -1,5 +1,6 @@
 <script setup lang="ts">
 import { ref, computed } from 'vue'
+import { useRouter } from 'vue-router'
 import { useI18n } from 'vue-i18n'
 import { useTheme } from '@/components/theme-provider'
 import { Button } from '@/components/ui/button'
@@ -15,6 +16,7 @@ interface NavigationItem {
   href: string
 }
 
+const router = useRouter()
 const { t } = useI18n()
 const { theme, setTheme } = useTheme()
 const isOpen = ref(false)
@@ -41,9 +43,10 @@ const openLoginDialog = () => {
 
 const handleLogout = async () => {
   try {
-    await auth.logout()
+    auth.logout()
     isOpen.value = false
-    // The redirect is now handled in the auth.logout() function
+    // Redirect to login page
+    router.push('/login')
   } catch (error) {
     console.error('Logout failed:', error)
   }