If an app starts windowed, it displays fine, but if it either starts fullscreen, or I switch it to fullscreen from windowed, only black is displayed (audio is still playing in the background, and I can exit the game with Esc normally, so it doesn't seem frozen).

neverball in the default repo can reproduce this easily for me. I've also compiled Xonotic (SDL2) and it exhibits the same thing. Games ran in Wine don't exhibit this.

Edit: This happens on an up-to-date Solus (Budgie) with Optimus, and also happens on a Live environment of MATE with Intel, so it doesn't seem to be related to DE/graphics/driver.