How to fix Multitouch Trackpad issues on MacBook Air?

I've recently acquired a new wireless trackpad (first USB-C model) to use with my MacBook Air and no gesture or multitouch is working. I can't even scroll a page with two fingers... It seems like any gesture that involves more than one finger is disabled even if that not the case when I look up at settings.

Also I've noticed that when I try to change any trackpad setting such as tracking speed, it affects the built-in trackpad but not this wireless trackpad. I tried to reproduce this on another older MacBook and I faced the exact same issue, whatever the trackpad is plugged in or not. I rebooted, forgot device and paired it again, it changed nothing...

Any idea what could cause this behavior ? Did I miss something while setting it up ?

[Re-Titled by Moderator]