I Bought POE2 on PS can I play on PC

I bought POE2 on Playstation and later realized i should have gotten it on PC when i go to manage account it shows i have no active keys so i wondering do i have to buy it on PC as well if i want to play or is it a bug and i just have to wait on Key.

Not a bug. I believe that is their arrangement with Sony. I had it on pc and had to do the same as you to play on PlayStation.