Thanks. The setting wasn't showing up at first, so I switched to Wayland.
It still wasn't showing up, so I disconnected and reconnected my controller. Then it appeared.
The box was unchecked, but the controller's touchpad still worked. I needed to check it, apply, and then uncheck it and apply again in order to turn off the touchpad.
I'm glad there's a way, although there are still some bugs that need to be worked out.
Disabling the touchpad in the settings will disable the touchpad for the controller, but it also disables the touchpad for my laptop which I do not want.