If I remember this correctly, you send a request with incorrect credentials either via javascript, or by sending the user to a "/logout"-endpoint where you disallow any authentication credentials, causing the browser to prompt the user for a new username and password. This not great in terms of UX and depending on something implicit for something as important as logging out does not seem great for security.

Why browsers do not have better functionality built in for authentication is something that's always been a bit baffling...