Can't approve Passwords and Keychain for iCloud for Windows

Beginning a few weeks ago, I was no longer able to use the iCloud Passwords extension for Edge on my main PC and a pop-up told me that I needed to enable Passwords in iCloud for Windows. Going in to iCloud for Windows, I found that Passwords and Keychain was off with an Approve... link underneath it. Clicking the link prompts a 2FA request on my iPhone and MacBook, which I authorized. I entered the code on my PC and it moved to the Signing In... screen, which then closed and there was no change to the Passwords and Keychain status. I've disabled VPNs and security software, and I've made sure that the PC is on the same network as my phone when doing the approval to no avail. iCloud for Windows is working just fine on my other PC and laptop. It's rather frustrating that there are no logs generated that end users have access to help diagnose the problem.

I've contacted Apple Support and they were supremely unhelpful as they told me to contact "Windows support" for help with this issue and then to come back to Apple with their results. I'm seeing that I'm not the only person having this problem. The PC in question is running Windows 10.