### 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/src/main/java/org/elasticsearch/xpack/ml/action/TransportStartDataFrameAnalyticsAction.java
timeout,
                            predicate.assignmentExplanation
                        )
                    );
                    if (predicate.assignmentExplanation != null) {
                        cancelAnalyticsStart(
                            task,
                            new ElasticsearchStatusException(
                                "Could not start data frame analytics task, timed out after [{}] waiting for task assignment. "
                                    + "Assignment explanation [{}]",
                                RestStatus.TOO_MANY_REQUESTS,
                                timeout,
                                predicate.assignmentExplanation
                            ),
                            listener
                        );
                    } else {
                        listener.onFailure(
                            new ElasticsearchException(
                                "Starting data frame analytics [{}] timed out after [{}]",
                                task.getParams().getId(),
                                timeout
                            )
                        );
                    }
                }
            }
        );
    }
    private static class StartContext {