Fair warning to anyone trying to follow Microsoft's "Advised solution" of messing with your partitions that it can just straight up cause your recovery partition to loose a necessary .wim file which will then, unless you then have a windows machine on the same update version from which you can harvest the .wim file, make it so that you're unable to reinitialize the windows recovery feature at all.
Not only that but even if you then just delete your recovery partition the update will still continue to fail.
If this happens it seems that your only recourse for getting a working recovery partition back is to literally wipe your drive and reinstall windows.
I personally spent all of yesterday dealing with this and dealing with trying to get a matching wim file with no luck.
So, thanks so much Microsoft. I sure enjoy you erasing hours of work while I'm asleep then destroying multiple days worth of my time because you can't configure your updates properly.
Yup, I don't have a computer science degree or anything but I'm not terrible with computers so I tried Microsoft's solution and I lost the Winre.wim file. So I couldn't re-enable WinRE.
Of course, then I couldn't use the recovery partition to reinstall Windows so I had to go online here to do that:
https://www.microsoft.com/en-us/software-download/windows10
Took 3 hours. PITA.
I will say, I don't know why. But after everything was reinstalled, I hit check for updates and it reinstalled everything from last Tuesday's update except for the one update we're talking about in this thread.
But then after it told me to reboot and I rebooted it and hit "Retry" to update again AND it actually installed the update with no problems. I'm not complaining but I have no idea why. So there is a little chance (lol) that reinstalling the OS does get the update to install.