### Description

This applies to the following APIs:
- [x] open anomaly detection
- [x] start datafeed
- [x] start data frame analytics job
- [x] start trained model deployment

Currently, if the operation takes longer than the configured `timeout`, the response status code is `500`.

With Kibana in mind, a `4xx` response would be more suitable as it will lead to showing more useful information to the user about why the request failed.

Looking at [RFC 9110](https://www.rfc-editor.org/rfc/rfc9110.html#name-408-request-timeout), it seems the most appropriate `4xx` code would be `408 Request Timeout`, even though the RFC describes a different situation. 

The alternative, `504 Gateway Timeout`, would be more appropriate for this situation but it wouldn't improve the user experience in Kibana.
x-pack/plugin/ml/qa/native-multi-node-tests/src/javaRestTest/java/org/elasticsearch/xpack/ml/integration/RunDataFrameAnalyticsIT.java
import org.elasticsearch.common.unit.ByteSizeValue;
import org.elasticsearch.index.IndexSettings;
import org.elasticsearch.index.query.QueryBuilders;
import org.elasticsearch.search.SearchHit;
import org.elasticsearch.xcontent.XContentType;
import org.elasticsearch.xpack.core.ml.action.GetDataFrameAnalyticsStatsAction;
import org.elasticsearch.xpack.core.ml.action.NodeAcknowledgedResponse;
import org.elasticsearch.xpack.core.ml.dataframe.DataFrameAnalyticsConfig;
import org.elasticsearch.xpack.core.ml.dataframe.DataFrameAnalyticsDest;
import org.elasticsearch.xpack.core.ml.dataframe.DataFrameAnalyticsSource;
import org.elasticsearch.xpack.core.ml.dataframe.DataFrameAnalyticsState;
import org.elasticsearch.xpack.core.ml.dataframe.analyses.OutlierDetection;
import org.junit.After;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import static org.hamcrest.Matchers.allOf;
import static org.hamcrest.Matchers.containsString;
import static org.hamcrest.Matchers.emptyString;
import static org.hamcrest.Matchers.equalTo;
import static org.hamcrest.Matchers.greaterThan;
import static org.hamcrest.Matchers.greaterThanOrEqualTo;
import static org.hamcrest.Matchers.hasItems;
import static org.hamcrest.Matchers.hasKey;
import static org.hamcrest.Matchers.is;
import static org.hamcrest.Matchers.lessThan;
import static org.hamcrest.Matchers.lessThanOrEqualTo;
import static org.hamcrest.Matchers.not;
import static org.hamcrest.Matchers.nullValue;
public class RunDataFrameAnalyticsIT extends MlNativeDataFrameAnalyticsIntegTestCase {