### Description

In #81809 we introduces a cluster setting that enables a pre-flight compatibility check for search requests going out from the coordinating node that checks if the request contains parts or features that are not supported on the previous minor version to quickly check full CCS compatibility for them. The error message the caller gets when e.g. using an aggregation that was just recently added could be improved. Currently the error message itself reads something like:

```
[class org.elasticsearch.action.search.SearchRequest] is not compatible with version 8.1.0 and the 'search.check_ccs_compatibility' setting is enabled.
```

The stack trace contains more information about e.g. the NamedWriteable that triggered the check to fail, but we might be able to surface more information in the error message itself.
modules/lang-mustache/src/internalClusterTest/java/org/elasticsearch/script/mustache/SearchTemplateIT.java
import org.elasticsearch.TransportVersion;
import org.elasticsearch.action.admin.cluster.storedscripts.GetStoredScriptResponse;
import org.elasticsearch.action.bulk.BulkRequestBuilder;
import org.elasticsearch.action.search.SearchRequest;
import org.elasticsearch.common.bytes.BytesArray;
import org.elasticsearch.common.settings.Settings;
import org.elasticsearch.plugins.Plugin;
import org.elasticsearch.script.ScriptType;
import org.elasticsearch.search.DummyQueryParserPlugin;
import org.elasticsearch.search.SearchService;
import org.elasticsearch.test.ESSingleNodeTestCase;
import org.elasticsearch.xcontent.XContentType;
import org.elasticsearch.xcontent.json.JsonXContent;
import org.junit.Before;
import java.io.IOException;
import java.util.Collection;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.concurrent.ExecutionException;
import static org.elasticsearch.test.hamcrest.ElasticsearchAssertions.assertAcked;
import static org.elasticsearch.test.hamcrest.ElasticsearchAssertions.assertHitCount;
import static org.elasticsearch.xcontent.XContentFactory.jsonBuilder;
import static org.hamcrest.Matchers.containsString;
import static org.hamcrest.Matchers.equalTo;
/**
 * Full integration test of the template query plugin.
 */
public class SearchTemplateIT extends ESSingleNodeTestCase {