### 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/DatafeedJobsIT.java
"composite bucket ["
                        + compositeBucket.getTimestamp()
                        + "] ["
                        + compositeBucket.getEventCount()
                        + "] does not equal"
                        + " scroll bucket ["
                        + scrollBucket.getTimestamp()
                        + "] ["
                        + scrollBucket.getEventCount()
                        + "]",
                    compositeBucket.getEventCount(),
                    equalTo(scrollBucket.getEventCount())
                );
            } catch (AssertionError ae) {
                String originalMessage = ae.getMessage();
                try {
                    SearchSourceBuilder builder = new SearchSourceBuilder().query(
                        QueryBuilders.rangeQuery("time")
                            .gte(scrollBucket.getTimestamp().getTime())
                            .lte(scrollBucket.getTimestamp().getTime() + TimeValue.timeValueHours(1).getMillis())
                    ).size(10_000);
                    SearchHits hits = client().search(new SearchRequest().indices(indexName).source(builder)).actionGet().getHits();
                    fail("Hits: " + Strings.arrayToDelimitedString(hits.getHits(), "\n") + " \n failure: " + originalMessage);
                } catch (ElasticsearchException ee) {
                    fail("could not search indices for better info. Original failure: " + originalMessage);
                }
            }
        }
    }
    private void assertDatafeedStats(String datafeedId, DatafeedState state, String jobId, Matcher<Long> searchCountMatcher) {