### 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
expectThrows(ResponseException.class, () -> client().performRequest(new Request("GET", indexName + "/_alias/" + readAliasName)));
        expectThrows(ResponseException.class, () -> client().performRequest(new Request("GET", indexName + "/_alias/" + writeAliasName)));
        client().performRequest(new Request("DELETE", MachineLearning.BASE_PATH + "anomaly_detectors/" + jobId));
    }
    public void testMultiIndexDelete() throws Exception {
        String jobId = "multi-index-delete-job";
        String indexName = AnomalyDetectorsIndexFields.RESULTS_INDEX_PREFIX + AnomalyDetectorsIndexFields.RESULTS_INDEX_DEFAULT;
        createFarequoteJob(jobId);
        
        
        Request extraIndex1 = new Request("PUT", indexName + "-001");
        extraIndex1.setJsonEntity("""
            {
              "aliases": {
                "%s": {
                  "is_hidden": true,
                  "filter": {
                    "term": {
                      "%s": "%s"
                    }
                  }
                }
              }
            }""".formatted(AnomalyDetectorsIndex.jobResultsAliasedName(jobId), Job.ID, jobId));
        client().performRequest(extraIndex1);
        Request extraIndex2 = new Request("PUT", indexName + "-002");
        extraIndex2.setJsonEntity("""
            {
              "aliases": {
                "%s": {