The current way of determining GTK_THEME_VARIANT (and based on that APPIMAGE_GTK_THEME) is to use the gtk-theme setting:

https://github.com/linuxdeploy/linuxdeploy-plugin-gtk/blob/1f054c88fd3f0d9ee46b5d5079b4a3b31d4c051e/linuxdeploy-plugin-gtk.sh#L211-212

On my (Ubuntu 22.10) system,

gsettings get org.gnome.desktop.interface gtk-theme

returns Yaru-purple, which doesn't give any indication if I use dark mode or not, whereas

gsettings get org.gnome.desktop.interface color-scheme

returns prefer-dark which is what seems relevant.

So I would suggest replacing gtk-theme by color-scheme on that line. Or why is the current version preferable?