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/auth/UserProfile.vue

@@ -1,5 +1,6 @@
 <script setup lang="ts">
 import { computed } from 'vue'
+import { useRouter } from 'vue-router'
 import { Button } from '@/components/ui/button'
 import { Card, CardContent, CardDescription, CardHeader, CardTitle } from '@/components/ui/card'
 import { Badge } from '@/components/ui/badge'
@@ -7,15 +8,13 @@ import { User, LogOut, Settings } from 'lucide-vue-next'
 import { auth } from '@/composables/useAuth'
 import { toast } from 'vue-sonner'
 
+const router = useRouter()
 const userDisplay = computed(() => auth.userDisplay.value)
 
-async function handleLogout() {
-  try {
-    await auth.logout()
-    toast.success('Logged out successfully')
-  } catch (error) {
-    toast.error('Failed to logout')
-  }
+function handleLogout() {
+  auth.logout()
+  toast.success('Logged out successfully')
+  router.push('/login')
 }
 </script>