However, it seems you could just as easily define the extension next to the given:

That would mean requiring to define the extension for each instance over and over again; although that is still the case in the provided example.

A better example would be this:

trait Functor[F[_]]:
  extension [A](fa: F[A])
    def map[B](f: A => B): F[B]

    final def as[B](b: B): F[A] = fa.map(_ => b)
end Functor

object List:
  given Functor[List] with:
    extension [A](la: List[A])
      override def map[B](f: A => B): List[B] =
        ...
end List

List(1, 2, 3).as("Foo")

The as extension method would be available out of the box.

Although, I personally think most libraries will continue to provide the extensions on a different syntax object to be imported.