feat: Enhance logout functionality and routing in authentication system

- Integrate `useRouter` in `UserProfile.vue` and `useAuth.ts` to manage navigation after logout.
- Update `handleLogout` in `Navbar.vue` to reflect that redirection is now handled within the `auth.logout()` function.

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'
@@ -7,6 +8,7 @@ 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() {

src/components/layout/Navbar.vue

@@ -43,6 +43,7 @@ const handleLogout = async () => {
   try {
     await auth.logout()
     isOpen.value = false
+    // The redirect is now handled in the auth.logout() function
   } catch (error) {
     console.error('Logout failed:', error)
   }

src/composables/useAuth.ts

@@ -1,4 +1,5 @@
 import { ref, computed } from 'vue'
+import { useRouter } from 'vue-router'
 import { lnbitsAPI, type User, type LoginCredentials, type RegisterData } from '@/lib/api/lnbits'
 
 const currentUser = ref<User | null>(null)
@@ -6,6 +7,7 @@ const isLoading = ref(false)
 const error = ref<string | null>(null)
 
 export function useAuth() {
+  const router = useRouter()
   const isAuthenticated = computed(() => !!currentUser.value)
 
   /**
@@ -82,6 +84,8 @@ export function useAuth() {
     } finally {
       currentUser.value = null
       error.value = null
+      // Redirect to login page after logout
+      router.push('/login')
     }
   }