Scala 2.13 - Use ADT to extend a sealed trait scala

Question

I have seen some examples to use ADT to extend data types to fit into either of the options but I am little confused on how to implement it in this kind of use case. In case classes I would create them and just add extends TraitName but what about primitive data types?

My sealed trait is AEMExpectedPayload which could be Booolean, Int, String, Seq[String],Seq[Boolean], or Seq[Int].

I want to do something like this:

sealed trait StringInt
String extends StringInt
Int extends StringInt

I see one way as:

sealed trait StringInt

case class Stringy(s : String) extends StringInt
case class Inty(s : Int) extends StringInt

However I wanted to confirm if this is the only way and nothing else?

Here's how I would want to use it:

val stringResult:StringInt = "test-string"
val intResult:StringInt = 22