Hi Aaron,
Thank you for sharing your question. I understand how annoying it is when the QR code scan during Windows setup just hangs, even if your Microsoft Authenticator app is working without problems in other cases. Generally, this happens because of problems pairing your device or with your internet during the first-time setup.
The reason this happens is that Windows makes use of the QR code to pair your PC with your Microsoft account to sign you in. If the scan won’t fully process, it's usually down to one of these things:
Your PC and phone aren't talking to each other properly via Bluetooth or internet.
Your Microsoft Authenticator app is an old version, or the time isn't synced right.
A short-term bug in the setup thingy.
Please follow these steps.
Get the newest update for the Microsoft Authenticator app and be sure your phone’s date and time gets set automatically.
Change internets: If you're on your phone’s internet, try Wi-Fi, and the other way around. Turn off VPN if it’s on.
Turn everything off and on again, and try scanning the QR code once more.
If scanning won’t work, tap “I can’t scan the QR code” on your PC and type the code manually into the Authenticator app.
Another way is to finish setting up using another way to prove it’s you (SMS or email) and put in the Authenticator later through account.microsoft.com/security.
May I also ask if you can check that Bluetooth is switched on and everything is on the internet? This should help get closer to the root cause.
I hope this answer is helpful, if you have any question, feel free to reply.
Best Regards,
Noel