Problem: Selecting "Microsoft Login" causes the Microsoft Store to launch the Gaming Services app. If the Gaming Services app is out of date and needs an update the Microsoft Store launches and reroutes to the update page, however, it will not update and the window will close and reopen rapidly.

Speculation: Force quitting the Microsoft Store app in Task Manager yields no result, so I assume the Minecraft Launcher does not understand that an update is needed and is relaunching to retry or doesn't know how to start an update.

Work Around: Force quitting the Launcher and updating the Gaming Services app fixed the issue, and it logged in just fine.

Notes: I had little issue fixing this problem because I have multiple monitors and some knowledge of using Windows 10. The Microsoft Store window opening and closing made using the monitor it was on impossible until I force to quit the Minecraft Launcher, which would have been impossible without a manual shutdown if you have one screen. The Gaming Services app still didn't automatically update after I closed the launcher so for some users, this might be extremely confusing and they might not know how to solve the problem. The fault primarily falls on the Microsoft Store app end, however, it still causes a major issue on the Minecraft Launcher so best to fix the problem here as well.