PS5 controller not visible on my PC's available bluetooth list

[Domestic Dom]

Recently I got myself a PS5, and I wanted to use the provided controller to play games on my PC that I already know will be compatible, but the controller doesn't want to appear as an available bluetooth device on my PC (before you ask, it indeed is in pairing mode and my PC is discoverable).

The controller works on the PS5 and my phone, and works via wired connection. I downloaded DS4Windows as suggested, updated all my drivers to the latest versions, yet it still refuses to appear. While I looked for solutions on multiple forums, 1 or 2 of them mentioned that the PS5 should be fully turned off, and all nearby devices should have their bluetooth turned off - STILL nothing.

My PC is brand new and doesn't have any bluetooth devices already connected to it, and the controller DOES appear on other devices and connect to them - like my phone, making it obvious that the issue is on the PC's side.

Can anyone tell me how am I supposed to fix this?