Because strings are iterable, and when you give the Set constructor an iterable object,¹ it loops through the values provided by the object's iterator and adds them to the set. In the case of strings, the string iterator iterates the strings code points — in your example, "1", "2", and "3". (For more about "code points" vs. "code units" and what a string is, read my blog post.)

If you want to add a string to a set, you have to do add separately or wrap it in another iterable (like an array):

// Add separately:
let set = new Set();
set.add("123");
console.log(set.size); // 1
console.log([...set]); // ["123"]

// Or wrap:
set = new Set(["123"]);
console.log(set.size); // 1
console.log([...set]); // ["123"]

¹ (or a primitive such as a string that coerces to an iterable object)

The Set constructor takes an iterable and takes every value of it.

Strings have an @@iterator property by default which makes them iterable:

const foo = "xyz";

console.log(...foo);

const [a, b, c] = foo;
console.log(a, b, c);

for (const char of foo)
  console.log(char);

Therefore, this is exactly what happens when you pass a string to a Set constructor - it draws every value just as it would with any other iterable:

const foo = "xyz";
const bar = [1, 2, 3]

console.log("set of string:", new Set(foo));
console.log("set of array :", new Set(bar));

<h1>Check the browser console</h1>