Just choose the “Keyboard (WASD) and Mouse” layout from the controller configuration. The right touchpad works well with R2 (the wand default) when waving around with the wand.
The latest stable Proton of the time worked with this game right away.
Ps. I wanted to add this information to this game’s info and install section Harry Potter and the Prisoner of Azkaban - Lutris but could not find anything else but “Suggest changes” and there was only the description of the game to be altered, so not suitable there.
Maybe some kind of additional “tinker” section could be added on Lutris.com for games?