An app flashes open and closes on Windows. Should I be worried?

A brief window isn't proof of malware. An updater or scheduled task could do that too. Try to identify the process before assuming the worst.

On Windows, Process Monitor from Microsoft Sysinternals can capture process start events. Start a capture, reproduce the flash, then stop it and look at process creation events around that time. Check the executable path and publisher, and search for the program name if you don't recognize it. A name alone isn't enough to tell whether a file is safe.

Deal with the account alert separately. An unrequested code can mean someone tried to sign in, but it doesn't prove they got in or that your computer caused it.

From a trusted device, change the affected account password and check its recent sign-in activity and recovery details. If you reuse that password elsewhere, change it there too. Secure your email account as well, since it can be used to reset other passwords. Don't share the verification code.

Run a full scan with Windows Security, and consider its offline scan if you're still concerned. Also review recently installed apps and browser extensions, especially anything from an unfamiliar source. Remove things you can identify as unwanted, rather than deleting random system files.

I wouldn't wipe the drive just because a window flashed. If you find strong evidence of a compromise, though, a clean Windows reinstall is an option. Back up needed files first and be careful not to restore suspicious programs along with them.