### 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
AnomalyDetectorsIndex.jobResultsAliasedName(jobId1),
                            jobId1
                        )
                    )
                );
                assertThat(aliasesResponse, containsString("""
                    "%s":{"is_hidden":true}""".formatted(AnomalyDetectorsIndex.resultsWriteAlias(jobId1))));
                assertThat(
                    aliasesResponse,
                    containsString(
                        """
                            "%s":{"filter":{"term":{"job_id":{"value":"%s"}}},"is_hidden":true}""".formatted(
                            AnomalyDetectorsIndex.jobResultsAliasedName(jobId2),
                            jobId2
                        )
                    )
                );
                assertThat(aliasesResponse, containsString("""
                    "%s":{"is_hidden":true}""".formatted(AnomalyDetectorsIndex.resultsWriteAlias(jobId2))));
            } catch (ResponseException e) {
                throw new AssertionError(e);
            }
        });
        
        String responseAsString = EntityUtils.toString(
            client().performRequest(new Request("GET", "/_cat/indices/" + AnomalyDetectorsIndexFields.RESULTS_INDEX_PREFIX + "*"))
                .getEntity()
        );
        assertThat(responseAsString, containsString(AnomalyDetectorsIndexFields.RESULTS_INDEX_PREFIX + "custom-" + indexName));
        assertThat(responseAsString, not(containsString(AnomalyDetectorsIndex.jobResultsAliasedName(jobId1))));