Thanks to the help I received in the comments I understood that maybe I was being too clever with the default trait method and the blanket impl. I could achieve the same in a much simpler way just by moving the method implementation to the trait impl:

pub trait IntoMyError {
  fn into_my_err(self, id: String) -> MyError;
}

impl<T: Into<anyhow::Error>> IntoMyError for T {
  fn into_my_err(self, id: String) -> MyError {
    MyError {
      id,
      kind: MyErrorKind::from(anyhow::Error::from(self)),
    }
  }
}