I can't get my Bluetooth devices to connect in Windows 10.  The problem has gotten much worse over time. Two devices are giving me grief: my mouse and my Bose QCII headphones. Both of them work correctly under Kubuntu Linux (dual booted), so this  isn't a hardware problem.

A while ago they both showed up in the Devices list that you can reach from Device Manager.  First the headphones disappeared and then the mouse.  The mouse was actually usable for a while but the headphones never were able to connect even though they were listed as paired.  They are still both detected; I know that because they show up in the Add a device section of Device Manager, where they try to connect but aren't able to.

One artifact that may or may not be relevant: both the mouse and the headphones show up twice, under different names.  The mouse is listed both as "BT 3.0" and "BT 5.2"; the headphones show up as "LE-Bose QQC II" and "Bose QC II".   If I turn the mouse off and on, I get a notice that it has appeared, but isn't able to pair.

There are several reports online about the problem with the Bose headphones and Windows 10, but no solutions.  I'm posting here because there are different experts here.