npm i firebase firebase-admin

app.ts

import * as admin from 'firebase-admin';

const serviceAccount = require('firebase-adminsdk.json');
admin.initializeApp({
    credential: admin.credential.cert(serviceAccount),
    databaseURL: "https://< project-name >.firebaseio.com"

});

async function authorize(req: Request, res: Response, next: NextFunction) {
    try {
        const token = req.headers.authorization;
        if(token !== undefined){
            const decodedToken = await admin.auth().verifyIdToken(token.split(' ')[1]);
            const userId = decodedToken.uid;
            console.log(userId);
            next();

        } else {
            throw new Error();
    
        }
        
    } catch (error) {
        res.status(204).send('need authorization');

    }

}

index.vue

<template>
  <div class="container">
    <div v-if="user">{{ user }}</div>
    <div v-else>offline</div>
    
    mail: <input type="text" v-model="mail">
    pass: <input type="text" v-model="password">
    <button v-on:click="login">login</button>
    <button v-on:click="logout">logout</button>

    <hr>
    name: <input type="text" v-model="name">
    <button v-on:click="register">register</button>



  </div>
</template>

<script>
import firebase from '../plugins/firebase';
import axios from '@nuxtjs/axios';

export default {
  data () {
    return {
      user : null,
      mail : "",
      password : "",
      name : ""

    }
  },

  methods : {
    async login() {
      const user = await firebase.auth().signInWithEmailAndPassword(this.mail, this.password);
      this.getUser();

    },

    async logout() {
      try {
        await firebase.auth().signOut();
        this.user = null;
      } catch (error) {
        console.error(error);

      }

    },

    async getUser() {
      const token = await firebase.auth().currentUser.getIdToken();
      console.log(token)
      const user = await this.$axios({
        method : 'GET',
        url : './api/user',
        headers : { 'Authorization' : `Bearer ${token}` }

      });

      this.user = user.data;

    }
    
  }

}
</script>


<style>

</style>