### 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/TransportStartDatafeedAction.java
public GetDatafeedRunningStateAction.Response.RunningState getRunningState() {
            synchronized (this) {
                if (datafeedRunner == null) {
                    
                    
                    
                    
                    
                    
                    return new GetDatafeedRunningStateAction.Response.RunningState(endTime == null, false, null);
                }
            }
            return new GetDatafeedRunningStateAction.Response.RunningState(
                endTime == null,
                datafeedRunner.finishedLookBack(this),
                datafeedRunner.getSearchInterval(this)
            );
        }
    }
    /**
     * Important: the methods of this class must NOT throw exceptions.  If they did then the callers
     * of endpoints waiting for a condition tested by this predicate would never get a response.
     */
    private static class DatafeedPredicate implements Predicate<PersistentTasksCustomMetadata.PersistentTask<?>> {
        private volatile Exception exception;
        private volatile String node = "";
        @Override
        public boolean test(PersistentTasksCustomMetadata.PersistentTask<?> persistentTask) {
            if (persistentTask == null) {
                return false;