There are two components current using Helloworld component save the value to localStorage and display the value from display from New component to display it. I tried using computed to get the data but it's still need to refresh to get the lastest value.
Here the example feel free to test or solve the problem >>> Example Sandbox
computed: {
token: {
  get: function () {
    return this.tokenValue;
  },
  set: function (id_token) {
    this.tokenValue = id_token;
    localStorage.setItem("Num1", id_token);
  },
},
},
 
    