clean up sample

Author: twsouthwick

aspnetcore/migration/fx-to-core/areas/owin.md

@@ -107,9 +107,7 @@ Register OWIN authentication as an ASP.NET Core authentication handler:
 ```csharp
 var builder = WebApplication.CreateBuilder(args);
 
-builder.Services
-    .AddSystemWebAdapters()
-    .AddAuthentication()
+builder.Services.AddAuthentication()
     .AddOwinAuthentication((owinApp, services) =>
     {
         owinApp.UseCookieAuthentication(new CookieAuthenticationOptions
@@ -124,6 +122,8 @@ var app = builder.Build();
 app.UseAuthentication();
 app.UseAuthorization();
 
+// Additional middleware or endpoint mapping
+
 app.Run();
 ```
 
@@ -168,13 +168,16 @@ For more information about authentication schemes and how they work in ASP.NET C
 Continue using the OWIN `IAuthenticationManager` interface:
 
 ```csharp
-var owinContext = HttpContext.GetOwinContext();
-var authManager = owinContext.Authentication;
+var authManager = HttpContext.GetOwinContext().Authentication;
 
 authManager.SignIn(identity);
 authManager.SignOut();
 ```
 
+### <xref:System.Security.Claims.ClaimsPrincipal.Current?displayProperty=nameWithType>
+
+If code is expecting to use <xref:System.Security.Claims.ClaimsPrincipal.Current?displayProperty=nameWithType>, then see <xref:migration/fx-to-core/areas/claimsprincipal-current> for options to enable setting that property.
+
 ## Migrating ASP.NET Framework Identity
 
 A common migration scenario involves ASP.NET Framework Identity with OWIN cookie authentication. This example shows how to maintain compatibility during migration.
@@ -199,15 +202,15 @@ Set up OWIN authentication with Identity services:
 ```csharp
 builder.Services
     .AddAuthentication()
-    .AddOwinAuthentication("SharedCookie", (app, services) =>
+    .AddOwinAuthentication("AppAuthenticationScheme", (app, services) =>
     {
         app.CreatePerOwinContext(ApplicationDbContext.Create);
         app.CreatePerOwinContext<ApplicationUserManager>(ApplicationUserManager.Create);
         app.CreatePerOwinContext<ApplicationSignInManager>(ApplicationSignInManager.Create);
 
         var dataProtector = services.GetDataProtector(
             "Microsoft.AspNetCore.Authentication.Cookies.CookieAuthenticationMiddleware",
-            "SharedCookie",
+            "AppAuthenticationScheme",
             "v2");
 
         app.UseCookieAuthentication(new CookieAuthenticationOptions