After adding the Flatpak backend and the Flathub source, I can't see the 0ad game from Flathub--only the Ubuntu package version. It's clearly supposed to be available, though. It's the first thing listed on https://flathub.org/apps.html. Everything else from Flathub that I've searched for is visible, except for 0ad.
I can reproduce, on my system it's: 0ad.desktop and on flathub com.play0ad.zeroad.desktop so it's not de-duplicated. Also the name is "0 A.D." so searching 0ad doesn't match :/ if you search "0 a." you'll find it.
Urgh. I'll go submit a patch to the 0 A.D. guys to change their AppStream ID to match what Flathub uses.
Submitted a patch at https://code.wildfiregames.com/D1186