As per the Sitecore documentation, the AuthenticationManager.Logout()
method does everything automatically.
When a user signs out from an external identity provider, Sitecore Identity redirects the user to the logout page of this identity provider, and then back to Sitecore. A full sign out from both Sitecore and the underlying identity provider usually cannot happen with a single request.
However, Sitecore Identity handles everything automatically when you use the AuthenticationManager.Logout()
method.
You can refer to the document for more details.
https://doc.sitecore.com/xp/en/developers/102/sitecore-experience-manager/understanding-sitecore-authentication-behavior-changes.html