Improve Docs by mentioning that Empty SecurityContext should be saved

Closes gh-12906

docs/modules/ROOT/pages/migration/servlet/session-management.adoc

@@ -11,6 +11,11 @@ In Spring Security 6, the default behavior is that the xref:servlet/authenticati
 Users now must explicitly save the `SecurityContext` with the `SecurityContextRepository` if they want the `SecurityContext` to persist between requests.
 This removes ambiguity and improves performance by only requiring writing to the `SecurityContextRepository` (i.e. `HttpSession`) when it is necessary.
 
+[NOTE]
+====
+Saving the context is also needed when clearing it out, for example during logout. Refer to this section to xref:servlet/authentication/session-management.adoc#properly-clearing-authentication[know more about that].
+====
+
 To opt into the new Spring Security 6 default, the following configuration can be used.
 
 include::partial$servlet/architecture/security-context-explicit.adoc[]

docs/modules/ROOT/pages/servlet/authentication/logout.adoc

@@ -139,6 +139,7 @@ If not configured a status code 200 will be returned by default.
 [[jc-logout-references]]
 == Further Logout-Related References
 
+- xref:servlet/authentication/session-management.adoc#properly-clearing-authentication[Properly Clearing Authentication When Explicit Save Is Enabled]
 - <<ns-logout, Logout Handling>>
 - xref:servlet/test/mockmvc/logout.adoc#test-logout[ Testing Logout]
 - xref:servlet/integrations/servlet-api.adoc#servletapi-logout[ HttpServletRequest.logout()]

docs/modules/ROOT/pages/servlet/authentication/session-management.adoc

@@ -54,6 +54,7 @@ But before you leave, consider if any of these use cases fit your application:
 * I want to <<understanding-session-management-components,Understand Session Management's components>>
 * I want to <<ns-concurrent-sessions,restrict the number of times>> a user can be logged in concurrently
 * I want <<store-authentication-manually,to store the authentication directly>> myself instead of Spring Security doing it for me
+* I am storing the authentication manually and I want <<properly-clearing-authentication,to remove it>>
 * I am using <<the-sessionmanagementfilter, `SessionManagementFilter`>> and I need <<moving-away-from-sessionmanagementfilter,guidance on moving away from that>>
 * I want to store the authentication <<customizing-where-authentication-is-stored,in something other than the session>>
 * I am using a <<stateless-authentication, stateless authentication>>, but <<storing-stateless-authentication-in-the-session,I'd still like to store it in the session>>
@@ -168,12 +169,6 @@ By default, Spring Security stores the security context for you in the HTTP sess
 
 First, you need to create an implementation of `SecurityContextRepository` or use an existing implementation like `HttpSessionSecurityContextRepository`, then you can set it in `HttpSecurity`.
 
-[NOTE]
-====
-The above configuration sets the `SecurityContextRepository` on the `SecurityContextHolderFilter` and **participating** authentication filters, like `UsernamePasswordAuthenticationFilter`.
-To also set it in stateless filters, please see <<storing-stateless-authentication-in-the-session,how to customize the `SecurityContextRepository` for Stateless Authentication>>.
-====
-
 [[customizing-the-securitycontextrepository]]
 .Customizing the `SecurityContextRepository`
 ====
@@ -220,6 +215,12 @@ open fun filterChain(http: HttpSecurity): SecurityFilterChain {
 ----
 ====
 
+[NOTE]
+====
+The above configuration sets the `SecurityContextRepository` on the `SecurityContextHolderFilter` and **participating** authentication filters, like `UsernamePasswordAuthenticationFilter`.
+To also set it in stateless filters, please see <<storing-stateless-authentication-in-the-session,how to customize the `SecurityContextRepository` for Stateless Authentication>>.
+====
+
 If you are using a custom authentication mechanism, you might want to <<store-authentication-manually,store the `Authentication` by yourself>>.
 
 [[store-authentication-manually]]
@@ -267,6 +268,32 @@ class LoginRequest {
 And that's it.
 If you are not sure what `securityContextHolderStrategy` is in the above example, you can read more about it in the <<use-securitycontextholderstrategy, Using `SecurityContextStrategy` section>>.
 
+[[properly-clearing-authentication]]
+=== Properly Clearing an Authentication
+
+If you are using Spring Security's xref:servlet/authentication/logout.adoc[Logout Support] then it handles a lot of stuff for you including clearing and saving the context.
+But, let's say you need to manually log users out of your app. In that case, you'll need to make sure you're clearing and saving the context properly.
+
+Now, you might already be familiar with clearing the `SecurityContextHolder` by doing `SecurityContextHolderStrategy#clearContext()`.
+That's great, but if your app requires an xref:migration/servlet/session-management.adoc#_require_explicit_saving_of_securitycontextrepository[explicit save of the context], simply clearing it isn't enough.
+The reason is that it doesn't remove it from the `SecurityContextRepository`, which means the `SecurityContext` could still be available for the next requests, and we definitely don't want that.
+
+To make sure the authentication is properly cleared and saved, you can invoke {security-api-url}/org/springframework/security/web/authentication/logout/SecurityContextLogoutHandler.html[the `SecurityContextLogoutHandler`] which does that for us, like so:
+
+====
+.Java
+[source,java,role="primary"]
+----
+SecurityContextLogoutHandler handler = new SecurityContextLogoutHandler(); <1>
+handler.logout(httpServletRequest, httpServletResponse, null); <2>
+----
+====
+
+<1> Create a new instance of `SecurityContextLogoutHandler`
+<2> Call the `logout` method passing in the `HttpServletRequest`, `HttpServletResponse` and a `null` authentication because it is not required for this handler.
+
+It's important to remember that clearing and saving the context is just one piece of the logout process, therefore we recommend having Spring Security take care of it.
+
 [[stateless-authentication]]
 === Configuring Persistence for Stateless Authentication