### 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
client().performRequest(new Request("GET", MachineLearning.BASE_PATH + "anomaly_detectors/" + jobId));
            
            
            String aliases = getAliases();
            assertThat(aliases, containsString(expectedReadAliasString));
            assertThat(aliases, containsString(expectedWriteAliasString));
        } catch (ResponseException missingJobException) {
            
            assertThat(missingJobException.getResponse().getStatusLine().getStatusCode(), equalTo(404));
            
            String aliases = getAliases();
            assertThat(aliases, not(containsString(expectedReadAliasString)));
            assertThat(aliases, not(containsString(expectedWriteAliasString)));
        }
        assertEquals(numThreads, recreationGuard.get());
    }
    private String getAliases() throws IOException {
        final Request aliasesRequest = new Request("GET", "/_aliases");
        
        
        aliasesRequest.setOptions(RequestOptions.DEFAULT.toBuilder().setWarningsHandler(warnings -> {
            if (warnings.isEmpty()) {
                return false;
            } else if (warnings.size() > 1) {
                return true;
            } else {
                return warnings.get(0).startsWith("this request accesses system indices:") == false;