[Test] Enable logging for AmazonHttpClient (elastic#116560) (elastic#116702)

If sending request fails locally without reaching the server, the
retryable exception is logged differently. This PR enables the logging
for this scenario.

Relates: elastic#88841 Relates: elastic#101608
(cherry picked from commit 5204902)

# Conflicts:
#	modules/repository-s3/src/internalClusterTest/java/org/elasticsearch/repositories/s3/S3BlobStoreRepositoryTests.java

Author: ywangd

modules/repository-s3/src/internalClusterTest/java/org/elasticsearch/repositories/s3/S3BlobStoreRepositoryTests.java

@@ -188,7 +188,10 @@ protected Settings nodeSettings(int nodeOrdinal, Settings otherSettings) {
     }
 
     @Override
-    @TestIssueLogging(issueUrl = "https://github.com/elastic/elasticsearch/issues/88841", value = "com.amazonaws.request:DEBUG")
+    @TestIssueLogging(
+        issueUrl = "https://github.com/elastic/elasticsearch/issues/88841",
+        value = "com.amazonaws.request:DEBUG,com.amazonaws.http.AmazonHttpClient:TRACE"
+    )
     public void testRequestStats() throws Exception {
         super.testRequestStats();
     }
@@ -234,8 +237,10 @@ public void testAbortRequestStats() throws Exception {
         assertEquals(assertionErrorMsg, mockCalls, sdkRequestCounts);
     }
 
-    @TestIssueLogging(issueUrl = "https://github.com/elastic/elasticsearch/issues/101608", value = "com.amazonaws.request:DEBUG")
-    @AwaitsFix(bugUrl = "https://github.com/elastic/elasticsearch/issues/101608")
+    @TestIssueLogging(
+        issueUrl = "https://github.com/elastic/elasticsearch/issues/101608",
+        value = "com.amazonaws.request:DEBUG,com.amazonaws.http.AmazonHttpClient:TRACE"
+    )
     public void testMetrics() throws Exception {
         // Create the repository and perform some activities
         final String repository = createRepository(randomRepositoryName(), false);