How do I keep my compose multiplattform app on top of fullscreen program?

Question

I am developing a desktop app using JetBrains Compose Multiplattform which i want to overlay over all my active applications.

It works over non-Fullscreen programs using just the following code:

fun main() = application {
  Window(
    onCloseRequest = ::exitApplication,
    undecorated = true,
    alwaysOnTop = true,
    //... further configuration
  ) {
    // window content
  }
}

What I cannot get to work is to show my overlay over full-screen applications (e.g. Counter-Strike, Valorant, etc.)

---

I don't really have seen any sources that could help on that topic.

I cannot use any Windows only solutions because I want to distribute the app to MacOS and Linux once I am finished.