### 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(entityAsMap(flushResponse), hasEntry("flushed", true));
        closeJob(jobId);
        String stats = EntityUtils.toString(
            client().performRequest(new Request("GET", "_ml/anomaly_detectors/" + jobId + "/_stats")).getEntity()
        );
        
        assertThat(stats, containsString("\"latest_record_timestamp\":1561941000000"));
        assertThat(stats, containsString("\"out_of_order_timestamp_count\":0"));
        assertThat(stats, containsString("\"processed_record_count\":3"));
        client().performRequest(new Request("DELETE", MachineLearning.BASE_PATH + "anomaly_detectors/" + jobId));
    }
    public void testDeleteJob_TimingStatsDocumentIsDeleted() throws Exception {
        String jobId = "delete-job-with-timing-stats-document-job";
        String indexName = AnomalyDetectorsIndexFields.RESULTS_INDEX_PREFIX + AnomalyDetectorsIndexFields.RESULTS_INDEX_DEFAULT;
        createFarequoteJob(jobId);
        assertThat(
            EntityUtils.toString(client().performRequest(new Request("GET", indexName + "/_count")).getEntity()),
            containsString("\"count\":0")
        );  
        openJob(jobId);
        Request postDataRequest = new Request("POST", MachineLearning.BASE_PATH + "anomaly_detectors/" + jobId + "/_data");
        
        postDataRequest.setOptions(POST_DATA);
        postDataRequest.setJsonEntity("""
            { "airline":"LOT", "response_time":100, "time":"2019-07-01 00:00:00Z" }""");
        client().performRequest(postDataRequest);
        postDataRequest.setJsonEntity("""
            { "airline":"LOT", "response_time":100, "time":"2019-07-01 02:00:00Z" }""");
        client().performRequest(postDataRequest);
        Response flushResponse = client().performRequest(