TypeScript conditional types with generics and objects

I have the following code:

type Id = string | number;

type ObjectId<T extends Id> = {
  id: T;
};

type ValidObjectId = ObjectId<string> | ObjectId<number>

type ReverseId<T extends ValidObjectId> = T['id'] extends number ? string : number;

function encodeObjectId<T extends ObjectId<number>>(
  obj: T
): ReverseId<T> {
  const id = obj.id;

  // Why does the following does not accept a string type?
  // As it's the reverse of type number, because of the `ReverseId` type, it should be working.
  return id.toString();
}

^{Playground link.}

In it, I have the type ReverseId, which converts the type of the id property. For example, if the given object id property has a number type, it will return string; and if the given object's id property has a string type, the number type will be returned.

And that actually works:

type Id = string | number;

type ObjectId<T extends Id> = {
  id: T;
};

type ValidObjectId = ObjectId<string> | ObjectId<number>

type ReverseId<T extends ValidObjectId> = T['id'] extends number ? string : number;

// The `t` constant has a `number` type, which is the "reverse" of the `string`
// type, used in the given `ObjectId`.
const t: ReverseId<ObjectId<string>> = 1;

^{Playground link.}

The problem is: when the ObjectId comes from a generic, as we saw in the encodeObjectId function in the first example, the type does not work.

Is there a way to solve this problem using conditional types?