It fails to install on my pc

Define "fails". What happens? Are you sure your Bluetooth is working and running stock drivers? What OS? Screenshots? Info, info, info!

Intel 9560 running intel drivers and working fine (I connect bt earbuds from time to time)
Windows 10 LTSC

This happens when no working Bluetooth radio is detected. Make sure that you run stock drivers (no SCP and alike) and that it's actually turned on. Nothing more I can recommend.

Efectively, it worked fine when I turned on BT (always turn it off when I dont use it)

After finishing setup, clicking on "Show next steps" didnt do anything,but lurking on the site, I followd this:
https://forums.vigem.org/topic/357/bthps3-post-setup-instructions

The pad works fine, but only wired. How am I supposed to pair it? Do I need some 3rd party software to pair the pad to the pc ?

The old SCP Pair Tool doesnt seem to work.

If everything works as expected Shibari will auto-pair every connected device to your main radio, assuming it is on and operational and has all the drivers required in place.

So I plugged an old USB bt I had, and I remembered I had SCP installed (thought not as a service, I always started it manually),and used the uninstall tool and wiped all the scp stuff on device manager manually, restarted, and reinstalled BthPs3. Now it works wiressly.