If Steam is running in the background, it could be taking your controller input and remapping it to a keyboard and mouse input. You can quickly check by fully exiting Steam and seeing if your controller is detected correctly. If it is, you can try adding pcsx2 as a non-steam game like the other comment suggested (but then you would need to do this for every other non-steam game using a controller), or you could disable Steam Input for "Non-game controller layouts".
With your controller connected, open steam in the upper left, and open to Settings > Controller > Desktop Layout > Edit. From there, disable Steam Input, and see if PCSX2 starts detecting your controller as a controller instead of a mouse and keyboard.
They honestly feel a bit like a satirical version of North Korea by isolating themselves with certain policies, and making crazy threats to anyone they can.
If Steam is running in the background, it could be taking your controller input and remapping it to a keyboard and mouse input. You can quickly check by fully exiting Steam and seeing if your controller is detected correctly. If it is, you can try adding pcsx2 as a non-steam game like the other comment suggested (but then you would need to do this for every other non-steam game using a controller), or you could disable Steam Input for "Non-game controller layouts".
With your controller connected, open steam in the upper left, and open to Settings > Controller > Desktop Layout > Edit. From there, disable Steam Input, and see if PCSX2 starts detecting your controller as a controller instead of a mouse and keyboard.