Flattening an Either tree in Scala 3

flateither.scala

import scala.annotation.tailrec

type FlatEither[A] = A match
  case Either[l, r] => FlatEither[l] | FlatEither[r]
  case _ => A

@tailrec
def flatEither[A](a: A): FlatEither[A] = a match
  case e: Either[?, ?] => e match
    case Right(r) => flatEither(r)
    case Left(l) => flatEither(l)
  case _ => a


val flatSimple: Int | String = flatEither(Right(1).withLeft[String])
assert(flatSimple == 1)
val e: Either[Either[Boolean, String], Int] = Left(Right("string"))
val flat: Boolean | String | Int = flatEither(e)
assert(flat == "string")