iMac Bootcamp and Magic Mouse woes
Finally, I seem to have solved this!

@BernardWei kind of lead me in the right general direction by suggesting I download the drivers from Apple again. Well, "download" is putting it strongly. I naturally went here to get them (which is wrong): https://support.apple.com/downloads/bootcamp

The downloads I was seeing on the Apple support site are Bootcamp v5.x versions. Which, according to a help article I stumbled across, aren't for Win 10, but are for earlier Windows versions (7 and the likes), which probably explains my issues when trying to use it. Please correct me if I'm wrong.

I decided to give downloading the support software via the Bootcamp Assistant in macOS another go. I originally got the idea from here: https://support.apple.com/en-us/HT204923

Previous attempts had seen the software not download and give a rather ambiguous error. Turns out that I had skipped over the bit about it needing to be in a FAT32 format. I was trying to save the data onto an external harddrive which I'm guessing isn't (I haven't got it plugged in to check right now). I then tried using the only USB drive I had, which only had 1GB of space, and the Bootcamp Assistant then failed for a lack of space reason, understandably. Having family to blag a larger USB drive from is useful if you come into this situation.

Here's the steps I took, once I had a large enough FAT32 USB drive.


Boot into macOS
Open up the Bootcamp Assistant.
Go into the actions menu and select Download Windows Support Software.
Select your ready-to-go USB drive as the destination and start the download.
You may be prompted for a password. Double check what it's asking and enter it if you're comfortable.
Go and get a hot drink, this will take a little while.
Once done, reboot into Windows.
Navigate to your USB drive. Go to WindowsSupport/Bootcamp/Setup.exe and run that. 
Pick repair.
Find something to do for a few minutes while the drivers on your machine are repaired. You may, like me, see multiple balloons pop up telling you that Windows is getting each one of your Bluetooth devices ready, and then again when they're done. You may also see a console Window running a disk partitioning tool. Don't worry, I think it just sets the default start up disk. I could be wrong, but nothing seems a miss yet.
Once done, you'll be prompted to restart. Do so. Your computer may try to boot to macOS, so use the options key to choose Windows as normal.
When your Windows machine restarts, your Bluetooth devices should behave themselves as expected.


Voila!

It's been a long time getting here, but I'm hopeful my mouse shinanigans are over for the time being. I'll reopen this question if my mouse stops connecting again as before. But for now, this is resolved!

EDIT: 1 day later, mouse isn't connecting again, and requires a restart into macOS to get it going. Which is back where we were at the beginning. That's fine, at least I know after a couple of restarts I'll have a fully working mouse again. 

Another side effect of doing this was that my external harddrive that normally runs as the D drive got de-lettered, as it were. I did a small amount of panicking before coming acoss this guide which helped me discover that all my previous data wasn't gone, but just needed re-assigning a drive letter from diskmgmt.msc: https://www.makeuseof.com/tag/external-drive-not-recognized-this-is-how-to-fix-it-in-windows/