### 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
}
            DataFrameAnalyticsTaskState taskState = (DataFrameAnalyticsTaskState) persistentTask.getState();
            reason = taskState != null ? taskState.getReason() : reason;
            DataFrameAnalyticsState analyticsState = taskState == null ? DataFrameAnalyticsState.STOPPED : taskState.getState();
            switch (analyticsState) {
                case STARTED:
                    node = persistentTask.getExecutorNode();
                    return true;
                case STOPPING:
                    exception = ExceptionsHelper.conflictStatusException("the task has been stopped while waiting to be started");
                    return true;
                
                
                
                
                
                case STARTING:
                case STOPPED:
                    return false;
                case FAILED:
                default:
                    exception = ExceptionsHelper.serverError(
                        "Unexpected task state [{}] {}while waiting to be started",
                        analyticsState,
                        reason == null ? "" : "with reason [" + reason + "] "
                    );
                    return true;
            }
        }
    }