### 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
}
        });
    }
    private static String extractTaskId(Response response) throws IOException {
        String responseAsString = EntityUtils.toString(response.getEntity());
        Pattern matchTaskId = Pattern.compile(".*\"task\":.*\"(.*)\".*");
        Matcher taskIdMatcher = matchTaskId.matcher(responseAsString);
        assertTrue(taskIdMatcher.matches());
        return taskIdMatcher.group(1);
    }
    public void testDeleteJobAfterMissingIndex() throws Exception {
        String jobId = "delete-job-after-missing-index-job";
        String aliasName = AnomalyDetectorsIndex.jobResultsAliasedName(jobId);
        String indexName = AnomalyDetectorsIndexFields.RESULTS_INDEX_PREFIX + AnomalyDetectorsIndexFields.RESULTS_INDEX_DEFAULT;
        createFarequoteJob(jobId);
        
        String indicesBeforeDelete = EntityUtils.toString(
            client().performRequest(new Request("GET", "/_cat/indices/" + AnomalyDetectorsIndexFields.RESULTS_INDEX_PREFIX + "*"))
                .getEntity()
        );
        assertThat(indicesBeforeDelete, containsString(indexName));
        
        
        client().performRequest(new Request("DELETE", indexName));
        client().performRequest(new Request("DELETE", MachineLearning.BASE_PATH + "anomaly_detectors/" + jobId));
        
        String indicesAfterDelete = EntityUtils.toString(
            client().performRequest(new Request("GET", "/_cat/indices/" + AnomalyDetectorsIndexFields.RESULTS_INDEX_PREFIX + "*"))
                .getEntity()
        );