### 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
.getEntity()
        );
        assertThat(indicesBeforeDelete, containsString(indexName));
        Response response = client().performRequest(
            new Request("DELETE", MachineLearning.BASE_PATH + "anomaly_detectors/" + jobId + "?wait_for_completion=false")
        );
        
        String taskId = extractTaskId(response);
        Response taskResponse = client().performRequest(new Request("GET", "_tasks/" + taskId + "?wait_for_completion=true"));
        assertThat(EntityUtils.toString(taskResponse.getEntity()), containsString("\"acknowledged\":true"));
        
        String indicesAfterDelete = EntityUtils.toString(
            client().performRequest(new Request("GET", "/_cat/indices/" + AnomalyDetectorsIndexFields.RESULTS_INDEX_PREFIX + "*"))
                .getEntity()
        );
        assertThat(indicesAfterDelete, containsString(indexName));
        waitUntilIndexIsEmpty(indexName);
        
        expectThrows(
            ResponseException.class,
            () -> client().performRequest(new Request("GET", MachineLearning.BASE_PATH + "anomaly_detectors/" + jobId + "/_stats"))
        );
    }
    private void waitUntilIndexIsEmpty(String indexName) throws Exception {
        assertBusy(() -> {
            try {
                String count = EntityUtils.toString(client().performRequest(new Request("GET", indexName + "/_count")).getEntity());
                assertThat(count, containsString("\"count\":0"));
            } catch (Exception e) {
                fail(e.getMessage());