GH-9297: Improve ImapIdleChannelAdapter.callIdle() for cause

Fixes: #9297

For a normal `jakarta.mail.StoreClosedException: * BYE Jakarta Mail Exception: java.net.SocketException: Connection reset`
 the `ImapIdleChannelAdapter.callIdle()` results in a resubmission (and reconnection)
 with logging 'Failed to execute IDLE task. Will attempt to resubmit in 10000 milliseconds.'`
However, when `selectorExpression` is in used and that one is based on mail `Message` object,
we may fail with `FolderClosedException` which is wrapped to the `SpelEvaluationException` and some
other stack traces.
So, `jakarta.mail.MessagingException` might be deep in the cause chain.

* Fix `ImapIdleChannelAdapter` via introducing `getJakartaMailMessagingExceptionFromCause()` utility
method which searches for the `jakarta.mail.MessagingException` in cause chain.
* Rework `ImapIdleChannelAdapter.callIdle()` logic to rely on this new method

**Auto-cherry-pick to `6.3.x` & `6.2.x`**

Author: artembilan

spring-integration-mail/src/main/java/org/springframework/integration/mail/ImapIdleChannelAdapter.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.
@@ -36,6 +36,7 @@
 import org.springframework.integration.transaction.IntegrationResourceHolder;
 import org.springframework.integration.transaction.IntegrationResourceHolderSynchronization;
 import org.springframework.integration.transaction.TransactionSynchronizationFactory;
+import org.springframework.lang.Nullable;
 import org.springframework.messaging.MessagingException;
 import org.springframework.transaction.support.TransactionSynchronization;
 import org.springframework.transaction.support.TransactionSynchronizationManager;
@@ -200,22 +201,24 @@ private void callIdle() {
 			}
 			catch (Exception ex) {
 				publishException(ex);
-				if (this.shouldReconnectAutomatically
-						&& ex.getCause() instanceof jakarta.mail.MessagingException messagingException) {
-
-					//run again after a delay
-					logger.info(messagingException,
-							() -> "Failed to execute IDLE task. Will attempt to resubmit in "
-									+ this.reconnectDelay + " milliseconds.");
-					delayNextIdleCall();
-				}
-				else {
-					logger.warn(ex,
-							"Failed to execute IDLE task. " +
-									"Won't resubmit since not a 'shouldReconnectAutomatically' " +
-									"or not a 'jakarta.mail.MessagingException'");
-					break;
+				if (this.shouldReconnectAutomatically) {
+					jakarta.mail.MessagingException messagingException =
+							getJakartaMailMessagingExceptionFromCause(ex.getCause());
+
+					if (messagingException != null) {
+						//run again after a delay
+						logger.info(messagingException,
+								() -> "Failed to execute IDLE task. Will attempt to resubmit in "
+										+ this.reconnectDelay + " milliseconds.");
+						delayNextIdleCall();
+						continue;
+					}
 				}
+				logger.warn(ex,
+						"Failed to execute IDLE task. " +
+								"Won't resubmit since not a 'shouldReconnectAutomatically' " +
+								"or not a 'jakarta.mail.MessagingException'");
+				break;
 			}
 		}
 	}
@@ -256,6 +259,21 @@ private void delayNextIdleCall() {
 		}
 	}
 
+	@Nullable
+	private static jakarta.mail.MessagingException getJakartaMailMessagingExceptionFromCause(Throwable cause) {
+		if (cause == null) {
+			return null;
+		}
+		if (cause instanceof jakarta.mail.MessagingException messagingException) {
+			return messagingException;
+		}
+		Throwable nextCause = cause.getCause();
+		if (cause == nextCause) {
+			return null;
+		}
+		return getJakartaMailMessagingExceptionFromCause(nextCause);
+	}
+
 	private class MessageSender implements Consumer<Object> {
 
 		MessageSender() {