The actual solutions here are XDG Desktop Portals or Wayland protocols, the former of which are commonly used (<https://flatpak.github.io/xdg-desktop-portal/>) and the latter of which are unstable proposals (<https://gitlab.freedesktop.org/wlroots/wlr-protocols/-/blob/...>). Wayland clients don't do compositor detection like you're describing, to my knowledge.