I'm encouraged by the facts that Sony's game controller linux driver works with no signup, and that this announcement mentions needing a Steam account but says nothing about a PSN account.

This is disappointing, though:

some key features, like HDR, headset feedback, eye tracking, adaptive triggers, and haptic feedback (other than rumble), are not available when playing on PC.

We don't know. Sony added open source Linux drivers for their gamepads so I guess it's not completely out of the question.