why is my vue-router not rendering my files?

I tried to use the Vue-router in my Vue project.
I installed it with npm install vue-router@latest.
My problem right now is, that it isn`t working

My router.js file looks like this:

import Vue from 'vue';
import Router from 'vue-router';
import Home from './src/components/Home.vue'

Vue.use(Router);

export default new Router({
  routes: [
    {
      path: '/',
      name: 'Home',
      component: Home 
    },
  ],
});

then I want to import it into the App.vue file with the <router-view></router-view>tag, but here is the whole file:

<script setup>
import { RouterView } from 'vue-router';
</script>

<template>
    <router-view></router-view>
</template>

Here is also a picture from the file structure:

enter image description here

Home.vue is just the whole landingpage, but when I run the server with npm run dev, it just shows a white page. Does someone know what the problem here is?