Hello @GaetanGodart,
On the other nucleo (F401RE), I set everything as usual. I created the project in CubeIDE (1.15.1), set up the clock configuration, pinout, SPI, added my libraries, then selected the TouchGFX component and added a picture or something. It worked every time.
I tried the same method on the H7, (but with the newer 1.16.0 CubeIDE,) and it didn't work.
Eventually after my ~fifth failed attempt I gave a try to CubeMX (6.11.1). I created the project in it, set up everything I could, added touchgfx, then did everything else in CubeIDE and it worked. I don't really understand why, so if you can tell me where I can read about the official way to set it up, I would appreciate it.