After some research I've managed to fix this. Here's how:
1. Open Konsole
2. Run this command:
sudo apt install xserver-xorg-input-synaptics
(don't forget to enter your password :)
3. Reboot
That's basically it. After this you can open System Settings, go to Input Devices / Touchpad settings and further adjust Noise Cancellation if you really want to.
Here's a little video I made about it in Kdenlive (it was an excuse to spend some time learning the basics of Kdenlive, really :).
Makes me wonder why it isn't installed out of the box :|