### 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
private volatile Exception exception;
        private volatile String node = "";
        private volatile String assignmentExplanation;
        @Override
        public boolean test(PersistentTasksCustomMetadata.PersistentTask<?> persistentTask) {
            if (persistentTask == null) {
                return false;
            }
            PersistentTasksCustomMetadata.Assignment assignment = persistentTask.getAssignment();
            
            if (assignment != null && assignment.equals(JobNodeSelector.AWAITING_LAZY_ASSIGNMENT)) {
                return true;
            }
            String reason = "__unknown__";
            if (assignment != null
                && assignment.equals(PersistentTasksCustomMetadata.INITIAL_ASSIGNMENT) == false
                && assignment.isAssigned() == false) {
                assignmentExplanation = assignment.getExplanation();
                
                
                if (assignmentExplanation.contains(PRIMARY_SHARDS_INACTIVE)) {
                    return false;
                }
                exception = new ElasticsearchStatusException(
                    "Could not start data frame analytics task, allocation explanation [{}]",
                    RestStatus.TOO_MANY_REQUESTS,
                    assignment.getExplanation()
                );
                return true;