This is documented at Sharing cookies among apps with ASP.NET and ASP.NET Core. There is also a Cookie Sharing App Sample available.
In order to share cookies, you create a DataProtectionProvider
in each app and using a common/shared set of keys between the apps.
.AddCookie(options =>
{
options.Cookie.Name = ".SharedCookie";
options.Cookie.Domain = "example.com";
options.DataProtectionProvider =
DataProtectionProvider.Create(new DirectoryInfo("path-tokeys"));
});