It is working now! Using kernel 5.4.0-42-generic and adding the "i8042.nopnp=1 pci=nocrs" kernel parameters to grub made the touchpad work.
(I also tried the solution proposed by Ferenc in Bug #1861610. It didn't work, but I cannot be sure if only using the kernel parameter works, so if it doesn't look there).
It is working now! Using kernel 5.4.0-42-generic and adding the "i8042.nopnp=1 pci=nocrs" kernel parameters to grub made the touchpad work.
(I also tried the solution proposed by Ferenc in Bug #1861610. It didn't work, but I cannot be sure if only using the kernel parameter works, so if it doesn't look there).