Unfortunately, I stumbled upon this thread just a little too late, which meant that I had already reinstalled Windows. Now ,y keyboard is working properly, even without having to apply @Andrew's solution, but there's no such luck with the mouse... It just will not connect. Prior to the reinstall, it kept trying and failing. Now Windows just says Paired, but the bloody thing won't connect. There's no button to force a try in the UI either, but that may be because the device has to actually initiate the connection; not the computer. Unfortunately, uninstalling the updates mentioned above will not work, simply because they were applied as part of a big ol' cumulative update, and therefore cannot be uninstalled separately... The big menace here is that the mouse actually did work before Windows started applying updates... If only my Mighty Mouse wouldn't have had such a ridiculously short wire, it would have been possible to use it instead of the Magic Mouse 2 in Windows (as a temporary measure, one hopes), but now it really isn't... It really is kind of a shame that Microsoft felt the need to forcefully disable the mouse (or at least that's how I feel), even though it works just fine. The same was the case under Windows, until a few weeks ago. I guess I can only hope for improvement on the Windows side for this (i.e. a new update set out to fix this)...
Update 2018/04/02: After reinstalling Windows 10 twice (for which I use a fully automated image that contains every bit of boot camp related stuff one might need), I found that my situation is a bit quirkier still than what I describe above. The keyboard actually works fine until such a time as when I try to connect the mouse. After that, the keyboard goes into this connect/disconnect frenzy that it doesn’t want to come out of, even after restarting the system, with a full power-down in between.
The real problem here, then, seems to be the mouse. This is, in fact, true in more than one way. I can successfully use the keyboard when I attach the lightning cable; it’s just the bluetooth bit of things that makes matters complicated. As we all know, this workaround does not apply to the mouse, whereas it seems to be the instigator of the whole issue, at least on my end.
As for now, there is no real solution if you, like me, got the affected updates as part of a cumulated update. You see, the issue started when Microsoft released two updates which were meant to resolve bluetooth related issues (specifically bluetooth 4 and bluetooth 4 LE). Unfortunately, I can’t remember the exact knowledge base numbers for those. If you’ve been using Windows 10 quite extensively (i.e. before the cumulative update encompassing them got released), you may be able to remove the individual updates and then hiding them if they’re offered again (requires downloading a trouble shooter from Microsoft) so that they’re not reinstalled. However, if, like me, you got the affronting patches through the cumulative update of February (which brings the OS Build to 17.09) then you’re SOL. This is because you cannot uninstall the smaller updates mentioned above (since you never got them in the first place) and uninstalling the cumulative updates brings back a positive shedload of other issues you’d rather be without...
Those of you who’ve experienced success with older accessories, such as the Apple Wireless Keyboard: the issue seems to be caused by the bluetooth 4(/LE) preamble (part of the handshake). As the aforementioned devices do not use Bluetooth 4, this could be why they do work…
For the moment, the situation is out of our control. All we can do is wait for either a correcting update by Microsoft, or a bluetooth, mouse and keyboard driver update by Apple, so as to work around the issues presented by the security patches Microsoft released my Microsoft.
