According to ASP.NET Core documentation the method HttpContext.Authentication.SignOutAsync()
must delete the authentication cookie as well.
Maybe your case was to use ASP NET Core Identity authentication stuff like in my case
so, instead of using HttpContext.Authentication.SignOutAsync() or HttpContext.SignOutAsync() you can try to use API from ASP NET Identity:
SignInManager.SignOutAsync()
API from HttpContext didn't clear cookies with names starting with ".AspNetCore."
(to use SignInManager you need to bring in SignInMbanager by asp net core's DI)