How is the equality operator (==) overridden for the String type in your code?

In C#, for the string type, the == operator is already overridden in the standard library, and it compares the contents of the strings, not the object references. If you create your own type and want to override the == operator, you need to implement a static method operator == and usually also operator !=.

Example of overriding for your own type:

public class MyString
{
    private string _value;

    public MyString(string value) => _value = value;

    public static bool operator ==(MyString a, MyString b)
    {
        if (ReferenceEquals(a, b)) return true;
        if (a is null || b is null) return false;
        return a._value == b._value;
    }

    public static bool operator !=(MyString a, MyString b) => !(a == b);

    public override bool Equals(object obj) => this == obj as MyString;

    public override int GetHashCode() => _value?.GetHashCode() ?? 0;
}

For the built-in string, overriding is not required; it is enough to use ==, which compares the contents.