### 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
}
        }, finalListener::onFailure);
        
        ActionListener<StartContext> toValidateExtractionPossibleListener = ActionListener.wrap(startContext -> {
            new ExtractedFieldsDetectorFactory(parentTaskClient).createFromSource(
                startContext.config,
                ActionListener.wrap(extractedFieldsDetector -> {
                    startContext.extractedFields = extractedFieldsDetector.detect().v1();
                    toValidateDestEmptyListener.onResponse(startContext);
                }, finalListener::onFailure)
            );
        }, finalListener::onFailure);
        
        ActionListener<StartContext> startContextListener = ActionListener.wrap(startContext -> {
            
            startContext.config.getSource().getParsedQuery();
            
            sourceDestValidator.validate(
                clusterService.state(),
                startContext.config.getSource().getIndex(),
                startContext.config.getDest().getIndex(),
                null,
                SourceDestValidations.ALL_VALIDATIONS,
                ActionListener.wrap(aBoolean -> toValidateExtractionPossibleListener.onResponse(startContext), finalListener::onFailure)
            );
        }, finalListener::onFailure);
        
        ActionListener<DataFrameAnalyticsConfig> getConfigListener = ActionListener.wrap(
            config -> getProgress(
                config,