Mark response errors from @ExceptionHandler as handled

Also fix a couple of related issues:
- add AsyncRequestNotUsableException to the list of exceptions
that imply response issues.
- handle exceptions from @ExceptionHandler regardless of whether
thrown immediately or via Publisher.

Closes gh-32359

spring-web/src/main/java/org/springframework/web/util/DisconnectedClientHelper.java

@@ -1,5 +1,5 @@
 /*
- * Copyright 2002-2023 the original author or authors.
+ * Copyright 2002-2024 the original author or authors.
  *
  * Licensed under the Apache License, Version 2.0 (the "License");
  * you may not use this file except in compliance with the License.
@@ -39,7 +39,8 @@ public class DisconnectedClientHelper {
 			Set.of("broken pipe", "connection reset by peer");
 
 	private static final Set<String> EXCEPTION_TYPE_NAMES =
-			Set.of("AbortedException", "ClientAbortException", "EOFException", "EofException");
+			Set.of("AbortedException", "ClientAbortException",
+					"EOFException", "EofException", "AsyncRequestNotUsableException");
 
 	private final Log logger;