Ok, I have played a little since the provided answers are not 100% clear.
If you want to have a shallow copy and copy the methods too, you can use Object.create.
Again: If your object is simple enough, Object.create will be sufficient for you
const originalPerson = new Person("John");
originalPerson.address = new Address("Paris", "France");
const newPerson = Object.create(originalPerson);
/// this will be true
const isInstanceOf = newPerson instanceof Person;
//this will change the property of the new person ONLY
newPerson.name = "Peter";
//methods will work
newPerson.someMethod();
//methods will work even on nested objects instances
newPerson.address.anotherMethod();
// BUT if we change the city on any of the instances -  will change the address.city of both persons since we have done a shallow copy
newPerson.address.city = "Berlin";
I have created typescript playground (just remove the types) to show it works and the drawback with its usage - link to the playground
Another approach is the class itself to have a clone method and to be responsible for its own cloning logic. An example follows, along with a link to another playground
class Address {
  constructor(city, country) {
    this.city = city;
    this.country = country;
  }
  clone() {
    // no special logic, BUT if the address eveolves this is the place to change the clone behvaiour
    return Object.create(this);
  }
  getAddressDetails() {
    return `City: ${this.city} country ${this.country}`;
  }
}
class Person {
  constructor(name, address) {
    this.name = name;
    this.address = address;
  }
  clone() {
    const newInstance = Object.create(this);
    //clone all other class instances
    newInstance.address = this.address.clone();
    return newInstance;
  }
  getPersonDetails() {
    //calling internally address.getAddressDetails() ensures that the inner object methods are also cloned
    return `This is ${this.name}, I live in ${this.address.getAddressDetails()}`
  }
}
const originalAddress = new Address("Paris", "France");
const originalPerson = new Person("John", originalAddress);
const clonedPerson = originalPerson.clone();
clonedPerson.name = "Peter";
clonedPerson.address.city = "Berlin";
clonedPerson.address.country = "Germany";
// Log to console
console.log(`Original person: ${originalPerson.getPersonDetails()}`)
console.log(`Cloned person: ${clonedPerson.getPersonDetails()}`)