Hello,
You are running into a classic Windows account sign-in pane issue. The small grey window is the Microsoft account broker failing to load and closing instantly, often after a work or school account was previously connected. The quickest fix is to repair that broker so the sign-in UI can open normally.
Close Settings and any Microsoft apps. Press Start, type PowerShell, right click Windows PowerShell, choose Run as administrator, then accept the prompt. In the PowerShell window run these two commands, one at a time, pressing Enter after each:
taskkill /f /im AccountHost.exe
Get-AppxPackage Microsoft.AAD.BrokerPlugin -AllUsers | Foreach {Add-AppxPackage -DisableDevelopmentMode -Register "$($_.InstallLocation)\AppXManifest.xml"}
Restart the PC. Go to Settings > Accounts > Your info and choose Sign in with a Microsoft account instead, then try again to sign in with your personal Microsoft account. After you can open and complete that sign-in, try the ESU enroll flow once more.
If the sign-in window still blinks and closes after this repair, tell me. The next step would be to clear a leftover work account link in one place inside Accounts that can keep hijacking the broker, but I want to keep us on one clean fix at a time.