### 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
GetDataFrameAnalyticsStatsAction.Response.Stats stats = statsResponse.getResponse().results().get(0);
                dfaTask.setStatsHolder(
                    new StatsHolder(stats.getProgress(), stats.getMemoryUsage(), stats.getAnalysisStats(), stats.getDataCounts())
                );
                executeTask(dfaTask);
            }, dfaTask::setFailed);
            
            ActionListener<Boolean> indexCheckListener = ActionListener.wrap(
                ok -> executeAsyncWithOrigin(
                    client,
                    ML_ORIGIN,
                    GetDataFrameAnalyticsStatsAction.INSTANCE,
                    new GetDataFrameAnalyticsStatsAction.Request(params.getId()),
                    statsListener
                ),
                error -> {
                    Throwable cause = ExceptionsHelper.unwrapCause(error);
                    logger.error(
                        () -> format(
                            "[%s] failed to create internal index [%s]",
                            params.getId(),
                            InferenceIndexConstants.LATEST_INDEX_NAME
                        ),
                        cause
                    );
                    dfaTask.setFailed(error);
                }
            );