HERE IS A QUICK SIMPLE GUIDE YOU CAN FOLLOW

I was facing the same problem ( whenever i do a fresh windows install and i install vscode in it) the following steps worked for me.

1. Go to Extension Tab.
2. Type "@buildin" in search bar
3. Find "Microsoft Account" Extension.
4. Now disable it and again enable it.
5. Try to sign in NOW.

HOPEFULLY YOUR PROBLEM IS SOLVED 😊