### 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
);
        assertThat(responseAsString, containsString("\"count\":2"));
        
        client().performRequest(new Request("DELETE", MachineLearning.BASE_PATH + "anomaly_detectors/" + jobId2));
        responseAsString = getAliases();
        assertThat(responseAsString, not(containsString(AnomalyDetectorsIndex.jobResultsAliasedName(jobId2))));
        refreshAllIndices();
        responseAsString = EntityUtils.toString(
            client().performRequest(new Request("GET", "/_cat/indices/" + AnomalyDetectorsIndexFields.RESULTS_INDEX_PREFIX + "*"))
                .getEntity()
        );
        assertThat(responseAsString, not(containsString(AnomalyDetectorsIndexFields.RESULTS_INDEX_PREFIX + "custom-" + indexName)));
    }
    public void testCreateJobInSharedIndexUpdatesMapping() throws Exception {
        String jobTemplate = """
            {
              "analysis_config" : {
                    "detectors" :[{"function":"metric","field_name":"metric", "by_field_name":"%s"}]
                },
              "data_description": {}
            }""";
        String jobId1 = "create-job-in-shared-index-updates-mapping-job-1";
        String byFieldName1 = "responsetime";
        String jobId2 = "create-job-in-shared-index-updates-mapping-job-2";
        String byFieldName2 = "cpu-usage";
        putJob(jobId1, String.format(Locale.ROOT, jobTemplate, byFieldName1));
        
        Request getResultsMappingRequest = new Request(
            "GET",
            AnomalyDetectorsIndexFields.RESULTS_INDEX_PREFIX + AnomalyDetectorsIndexFields.RESULTS_INDEX_DEFAULT + "/_mapping"