Does Ubuntu support the ASUS trackpad of a ZenBook-14-UX?

I believe their trackpad is just a fancy way of enabling NumLock, so if it doesn't need any extra driver, (is plug-n-play), the trackpad shouldn't be a problem.

However, you may need to install Nvidia drivers.

If you want to make sure it is compatible you should delve into reviews and technical documentation. I would personally check if it's plug n play or if it requires extra software, as soon as it requires extra software, it will be incompatible with other OS.