If you're searching for something solid and zero lag, i recommand that bluetooth adapter. DS4 Windows is too fragile, and got too much issues. And only PS4 compatible : with that key you can convert every controller you want for playing on PC or PS4 or PS5, Series X, Switch etc.
I use it for my Retro-gaming Raspberry sometimes, then my PC...
https://www.walmart.com/ip/Wireless...S-Elite-Series-2-PS5-PS4-Switch-Pro/465625997
Now on PS5 you can make a pairing for your PS4 controller. Also the home button didn't worked before, now i'm happy than everything is functionnal.
But for my others pad and console, and PC (especially, yes i play some games on it i got for free lol) it's working perfectly. I was sceptic about the key but i don't regret at all to have brought it.
PS4 controller is a must, to be honest i found that the DS4 got better ergonomics to me than the DS5, but more durable stick from what i see (i use protections for it, and i prefers the sticks more flat so it's all ok) but it's my opinion.
Well i own one old controller with a Bluetooth key for PC but for having a good wireless PC controller, you got to put the price... The on i owned got an issue with the left analog going a bit on the right after not so much utilisations, i've made a test.
It's looking like that one but older from 7 years ago
https://www.amazon.nl/Draadloze-controller-vervanging-Vibration-oplaadbaar/dp/B08BLKNWH6/ref=sr_1_151?__mk_nl_NL=ÅMÅŽÕÑ&crid=3ACU6MSI7192U&keywords=bluetooth+controller+pc&qid=1664374567&qu=eyJxc2MiOiIzLjcxIiwicXNhIjoiMi43MiIsInFzcCI6IjIuMDAifQ==&sprefix=bluetooth+controller+pc,aps,92&sr=8-151