I don't want to hijacked this thread, but i have this EXACT same problem.
My controllers (one fake, one genuine) are working with a cable, but when i connect them over bluetooth, the controllers are detected (led in the controllers, device manager too) but no input detected in games or with the Windows tool..
I have an Intel AX200 card, so my bluetooth version is 5.1.
As I already commented in another thread the rumble code in Shibari (which is the responsible component) is not well tested and probably faulty. Watch the commits, if I get around to it I'll take a look at it.
I came across this thread when I realized some strange behavior with my combo of FireShock / ViGEm / Shibari causing occasional BSoD or causing my USB Host controller to crash, in this state I couldn't plug any new devices into my machine via USB. I was running FireShock 126.96.36.199, ViGEmBus 1.16.116, and Shibari 1.5.171 as a service.
When it worked, it worked great. But as I've been working on some video projects lately with long render times I had to uninstall it all so I wasn't risking system stability.
I don't use Bluetooth with my DS3, just a MicroUSB cable. Right now I have all of the above still uninstalled, but I'd like to get it back in place as this seems like the best solution for straight-forward PS3 controller usage.
Running Windows 10 Enterprise LTSC 2019, which corresponds to Build 1809. If it would help for testing, I can disable driver signature enforcement and try using the FireShock unsigned CI drivers 188.8.131.52 and see if I get similar symptoms.
If there's a better combo of drivers / software for PS3 dualshock usage, I'm game to try anything.
Edit: The error on the BSoD was DRIVER_POWER_STATE_FAILURE, seemed partially similar.
I remembered things were normal when using scp drivers/motioninjoy on win 7/win xp, the rumble are just normal as console liked vibrations especially with directinput configuration, but it's weird now with xinput, why no more directinput support on win10?
There was definitely no DirectInput rumble support via SCP. SCP and PCSX2 in combination with the modified LilyPad plugin is probably what you meant/experienced.