I use a DualShock 4 on Arch with Hyprland.

By default for libinput, the controller touchpad always controls the mouse cursor. So I needed to disable that.

In my desktop configuration, my mouse cursor hides itself after 5 seconds of inactivity. I’ve found that Steam Input doesn’t register as mouse movement, despite successfully moving the cursor, so the cursor remains invisible. I have a (Hyprland specific) command I run to disable that config option temporarily, so that way I can use Steam Input to control the mouse cursor.

The right joystick mapping to it sounds like Steam Input’s default “Desktop Configuration”. I’d check that to see. I personally have the desktop configuration pretty much empty, but I have the touchpad set to control my mouse cursor under “Guide Button Chord Configuration”, so if I hold the PS Logo I can move my cursor with that.