feat: Add logo and enhance login functionality

- Introduce a new logo asset for branding.
- Update LoginDialog.vue to include routing for successful login and registration.
- Modify Navbar.vue to integrate LoginDialog and manage its visibility.
- Revise Login.vue to update the logo and welcome title, along with routing enhancements post-login and registration.

src/components/auth/LoginDialog.vue

@@ -1,5 +1,6 @@
 <script setup lang="ts">
 import { ref, computed } from 'vue'
+import { useRouter } from 'vue-router'
 import { Dialog, DialogContent, DialogDescription, DialogHeader, DialogTitle } from '@/components/ui/dialog'
 import { Tabs, TabsContent, TabsList, TabsTrigger } from '@/components/ui/tabs'
 import { Button } from '@/components/ui/button'
@@ -18,6 +19,7 @@ interface Emits {
   (e: 'success'): void
 }
 
+const router = useRouter()
 defineProps<Props>()
 const emit = defineEmits<Emits>()
 
@@ -64,6 +66,8 @@ async function handleLogin() {
     toast.success('Login successful!')
     emit('success')
     handleClose()
+    // Redirect to home page after successful login
+    router.push('/')
   } catch (err) {
     error.value = err instanceof Error ? err.message : 'Login failed'
     toast.error('Login failed. Please check your credentials.')
@@ -89,6 +93,8 @@ async function handleRegister() {
     toast.success('Registration successful!')
     emit('success')
     handleClose()
+    // Redirect to home page after successful registration
+    router.push('/')
   } catch (err) {
     error.value = err instanceof Error ? err.message : 'Registration failed'
     toast.error('Registration failed. Please try again.')