PAYDAY 3 on PC supports the use of DualSense (PlayStation 5) controllers, however, in order for it to function correctly, you must install the PlayStation Accessories App from Sony, which will install drivers for your controller. It can be downloaded from the following URL:
https://controller.dl.playstation.net/controller/lang/en/2100004.html
Ensure that your controller's Firmware is up to date before attempting to play.
If you have connected your controller to your PC via Bluetooth and PAYDAY 3 does not recognise it, please try to connect your controller with a USB cable instead.