I can see it looks like you are using Vue 3 which requires a different syntax than Vue 2. There is no global $f7 variable in Vue 3. Follow the code I have here for main.js you need to tell Vue to use the Framework7 plugin.
Check that your main.js has the imported libraries.
import { createApp } from 'vue'
import Framework7 from 'framework7/lite-bundle';
import Framework7Vue from 'framework7-vue/bundle';
import App from './App.vue'
import '../node_modules/framework7/framework7-bundle.min.css';
Framework7.use(Framework7Vue)
const app = createApp(App)
app.mount('#app')
In your component then import f7 and create a notification.