Are you certain you installed the correct application? Plex Desktop’s current stable release is 1.47.1.3086-6c3d964f.
It sounds like you actually installed Plex HTPC (of which the current version is 1.19.1); that application isn’t intended to be controlled by a mouse (and is intended to be used full-screen).
Try sudo snap install plex-desktop. It may be more to your liking, if you’re looking for an actual desktop application.
