### 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
ExceptionsHelper.badRequestException(
                        "Unable to start because too many documents "
                            + "(more than 2^32) are included in the analysis. Consider downsampling."
                    )
                );
            } else {
                listener.onResponse(startContext);
            }
        }, listener::onFailure));
    }
    private void getProgress(DataFrameAnalyticsConfig config, ActionListener<List<PhaseProgress>> listener) {
        GetDataFrameAnalyticsStatsAction.Request getStatsRequest = new GetDataFrameAnalyticsStatsAction.Request(config.getId());
        executeAsyncWithOrigin(
            client,
            ML_ORIGIN,
            GetDataFrameAnalyticsStatsAction.INSTANCE,
            getStatsRequest,
            ActionListener.wrap(statsResponse -> {
                List<GetDataFrameAnalyticsStatsAction.Response.Stats> stats = statsResponse.getResponse().results();
                if (stats.isEmpty()) {
                    
                    listener.onFailure(ExceptionsHelper.missingDataFrameAnalytics(config.getId()));
                } else {
                    listener.onResponse(stats.get(0).getProgress());
                }
            }, listener::onFailure)
        );
    }
    private void checkDestIndexIsEmptyIfExists(
        ParentTaskAssigningClient parentTaskClient,