LE13 now has support for flatpak add-ons with the Chrome add-on experience where Kodi is stopped, the flatpak app runs, and when you exit the app Kodi is restarted. We already added the SteamLink flatpak. We'd prefer to see a Moonlight flatpak add-on (assuming it works) as this would have less maintenance and faster compile than dealing with Qt6 from source.
You could also investigate the LEIoT distro which coexists in the buildsystem as the base for a more minimal image. LEIoT drops all the background plumbing for Kodi (which you're probably not using) with a base image around 85MB in size (including Docker). You could drop docker and add moonlight-qt to ADDITIONAL_PACKAGES+= and see what happens or leave it and package the Qt6 things you need into a container (or be lazy and pull someone else's) .. there's lots of options.
NB: I'd suggest creating your own $DEVICE in the buildsystem else future changes we push will trample on yours in a rebase. I plan to drop current Rockchip devices after LE13 and reconfigure the buildsystem to have two new ones; a single 'arm' image (RK3288) and single 'aarch64' image (RK3328 thru RK3588) using a common kernel/patchset.