### 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(indicesAfterDelete, not(containsString(aliasName)));
        assertThat(indicesAfterDelete, not(containsString(indexName)));
        expectThrows(
            ResponseException.class,
            () -> client().performRequest(new Request("GET", MachineLearning.BASE_PATH + "anomaly_detectors/" + jobId + "/_stats"))
        );
    }
    public void testDeleteJobAfterMissingAliases() throws Exception {
        String jobId = "delete-job-after-missing-alias-job";
        String readAliasName = AnomalyDetectorsIndex.jobResultsAliasedName(jobId);
        String writeAliasName = AnomalyDetectorsIndex.resultsWriteAlias(jobId);
        String indexName = AnomalyDetectorsIndexFields.RESULTS_INDEX_PREFIX + AnomalyDetectorsIndexFields.RESULTS_INDEX_DEFAULT;
        createFarequoteJob(jobId);
        
        
        
        assertBusy(() -> {
            try {
                String aliases = EntityUtils.toString(client().performRequest(new Request("GET", "/_cat/aliases")).getEntity());
                assertThat(aliases, containsString(readAliasName));
                assertThat(aliases, containsString(writeAliasName));
            } catch (ResponseException e) {
                throw new AssertionError(e);
            }
        });
        
        
        client().performRequest(new Request("DELETE", indexName + "/_alias/" + readAliasName));
        client().performRequest(new Request("DELETE", indexName + "/_alias/" + writeAliasName));