Musescore won't activate Muse Sounds when installed on Linux via Flatpak

I'm trying to use the new Muse Hub/Muse Sounds on Linux Mint 21.1. I installed Muse Hub and all of the Muse Sounds packages, which installed into the default /srv/muse-hub/downloads/. I ran Musescore 4.0.0, which was already installed via Flatpak, and tried to activate Muse Sounds (View -> Playback Setup), but Muse Sounds is grayed-out and cannot be activated. I tried uninstalling everything (Musescore, Muse Hub, and Muse Sounds packages), deleting all configuration folders, reinstalling everything and trying again. Same result. I then tried the AppImage Musescore package, and it immediately found the Muse Sounds and could activate and use them. However, AppImages won't update through my OS's update system, and having been spoiled by Linux's awesome software update methods over the last 20 years, I really don't want to mess with the hassle of manually updating software packages. Is there a way to get the Flatpak version to recognize the Muse Sounds packages and activate them? I really don't want to have to use the AppImage. AppImages are such a pain.