Hello alpha_659, welcome to the Microsoft community, I'll be happy to help you today;
I understand that you are having problems connecting your PS4 controller to your PC;
Your PS4 must be turned off for you to be able to connect the controller to the PC;
Initially I recommend that I recommend controlling the settings;
Press Windows key + i and go to Bluetooth and other devices;
Click on View more devices;
Remove the Wireless Controller from the list;
You will need Steam to be able to use the controller:https://store.steampowered.com/about/?snr=1_4_4...
Now try the methods given in the video below:
https://www.youtube.com/watch?v=Zhy5GG1e81Q
Disclaimer: There are links to non-Microsoft sites. The pages appear to provide accurate and secure information. Watch out for ads on websites that may advertise products that are often classified as PUPs (Potentially Unwanted Goods). Thoroughly research any product advertised on the websites before deciding to download and install it.
Hope this helps, see you soon!