### 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, not(containsString(AnomalyDetectorsIndex.jobResultsAliasedName(jobId2))));
        { 
            String id = String.format(Locale.ROOT, "%s_bucket_%s_%s", jobId1, "1234", 300);
            Request createResultRequest = new Request("PUT", AnomalyDetectorsIndex.jobResultsAliasedName(jobId1) + "/_doc/" + id);
            createResultRequest.setJsonEntity(String.format(Locale.ROOT, """
                {"job_id":"%s", "timestamp": "%s", "result_type":"bucket", "bucket_span": "%s"}""", jobId1, "1234", 1));
            client().performRequest(createResultRequest);
            id = String.format(Locale.ROOT, "%s_bucket_%s_%s", jobId1, "1236", 300);
            createResultRequest = new Request("PUT", AnomalyDetectorsIndex.jobResultsAliasedName(jobId1) + "/_doc/" + id);
            createResultRequest.setJsonEntity(String.format(Locale.ROOT, """
                {"job_id":"%s", "timestamp": "%s", "result_type":"bucket", "bucket_span": "%s"}""", jobId1, "1236", 1));
            client().performRequest(createResultRequest);
            refreshAllIndices();
            responseAsString = EntityUtils.toString(
                client().performRequest(new Request("GET", MachineLearning.BASE_PATH + "anomaly_detectors/" + jobId1 + "/results/buckets"))
                    .getEntity()
            );
            assertThat(responseAsString, containsString("\"count\":2"));
            responseAsString = EntityUtils.toString(
                client().performRequest(new Request("GET", AnomalyDetectorsIndex.jobResultsAliasedName(jobId1) + "/_search")).getEntity()
            );
            assertThat(responseAsString, containsString("\"value\":2"));
        }
        { 
            String id = String.format(Locale.ROOT, "%s_bucket_%s_%s", jobId2, "1234", 300);
            Request createResultRequest = new Request("PUT", AnomalyDetectorsIndex.jobResultsAliasedName(jobId2) + "/_doc/" + id);
            createResultRequest.setJsonEntity(String.format(Locale.ROOT, """
                {"job_id":"%s", "timestamp": "%s", "result_type":"bucket", "bucket_span": "%s"}""", jobId2, "1234", 1));
            client().performRequest(createResultRequest);
            id = String.format(Locale.ROOT, "%s_bucket_%s_%s", jobId2, "1236", 300);