Bugged shared interaction of Bluetooth device with 2 Windows 10 OSes on same PC

I have 2 Windows 10 OSes on the same PC. If I pair a Bluetooth device to one of them, it works fine. But when I reboot to the second OS, there are already this device paired somehow. But I'm unable to connect to it. So I need to unpair it first, then pair and connect. But on the first OS, I have the same situation, and I need to unpair + pair again. I don't know where it's stored and why paired devices are visible to different OS on different drives. Is it possible to either share the same valid profile on both OSes or restrict pairing the device to only one OS?

Question by Sergey Senkov on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.