### 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/MlJobIT.java
Request createDoc3 = new Request("PUT", indexName + "/_doc/" + 456);
        createDoc3.setEntity(createDoc0.getEntity());
        client().performRequest(createDoc3);
        refreshAllIndices();
        
        assertThat(
            EntityUtils.toString(client().performRequest(new Request("GET", indexName + "/_count")).getEntity()),
            containsString("\"count\":2")
        );
        assertThat(
            EntityUtils.toString(client().performRequest(new Request("GET", indexName + "-001/_count")).getEntity()),
            containsString("\"count\":1")
        );
        assertThat(
            EntityUtils.toString(client().performRequest(new Request("GET", indexName + "-002/_count")).getEntity()),
            containsString("\"count\":1")
        );
        
        client().performRequest(new Request("DELETE", MachineLearning.BASE_PATH + "anomaly_detectors/" + jobId));
        refreshAllIndices();
        
        String indicesAfterDelete = EntityUtils.toString(
            client().performRequest(new Request("GET", "/_cat/indices/" + AnomalyDetectorsIndexFields.RESULTS_INDEX_PREFIX + "*"))
                .getEntity()
        );
        assertThat(indicesAfterDelete, containsString(indexName));
        
        assertThat(indicesAfterDelete, not(containsString(indexName + "-001")));
        assertThat(indicesAfterDelete, not(containsString(indexName + "-002")));
        assertThat(