I do have xdg-desktop-portal-gtk on Debian Stable, which is currently at 1.14.1-1. I’ll look around to see if there’s more documentation on this method, because I would prefer to not use the debug variables if possible.
Edit: I launched with GTK_DEBUG=interactive and I can see the theme inside the Flatpak gets set to Adwaita-empty instead of my actual theme, which does get properly returned via gsettings get org.gnome.desktop.interface gtk-theme