String literals vs string objects hashcode

I read that strings declared as literals are created on String Constant Pool String s1 = "Hello"; String s2 = "Hello"; -> This will not create a new object and will refer to the s1 reference.

And strings declared with new keyword are created on both Heap Memory and String Constant Pool String s3 = new String("Hello"); -> This will create a new object in the heap. But will it create a new constant in the String Constant Pool also or will it use the one from s1?

I have this following code. Hashcode for all s1, s2, and s3 are return as same.

public class question1 {

  public static void main(String[] args) {

    String s1 = "Hello";
    String s2 = "Hello";
    String s3 = new String("Hello");

    System.out.println(s1 == s2);
    System.out.println(s1 == s3); // not sure why false result, s3 will create a separate constant in the pool? There is already a constant with value "Hello" created by s1. Please confirm if s3 will again create a constant.
  }
}

I understant that == compares the object. Are there two "Hello" defined in the String Constant Pool, one from s1 and one from s3?