ASP.NET WebForms Authentication Logout, Cookie can still be used to access site

I have been banging my head against the wall and searching the web for this but I think I am having issues understanding the whole process of logging users out of an asp.net webforms application. The issue:
I am able to log in to my application and it uses cookies, so I have my cookie set in the browser.
here is the config forms authentication section,

How to consume and ASP.NET Membership database in ASP.NET Identity?

I have a couple of legacy ASP.NET web apps that share a database for ASP.NET Membership. I want to move to a microservices architecture utilizing .NET Core and IdentityServer4 and have the identity server in the new microservices ecosystem to use the existing ASP.NET Membership user store, but .NET Core doesn’t appear to support ASP.NET Membership at all.