### 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
ActionListener.wrap(
                    progress -> startContextListener.onResponse(new StartContext(config, progress)),
                    finalListener::onFailure
                )
            ),
            finalListener::onFailure
        );
        
        configProvider.get(id, getConfigListener);
    }
    private void validateSourceIndexHasAnalyzableData(StartContext startContext, ActionListener<StartContext> listener) {
        ActionListener<Void> validateAtLeastOneAnalyzedFieldListener = ActionListener.wrap(
            aVoid -> validateSourceIndexRowsCount(startContext, listener),
            listener::onFailure
        );
        validateSourceIndexHasAtLeastOneAnalyzedField(startContext, validateAtLeastOneAnalyzedFieldListener);
    }
    private void validateSourceIndexHasAtLeastOneAnalyzedField(StartContext startContext, ActionListener<Void> listener) {
        Set<String> requiredFields = startContext.config.getAnalysis()
            .getRequiredFields()
            .stream()
            .map(RequiredField::getName)
            .collect(Collectors.toSet());
        
        long nonRequiredFieldsCount = startContext.extractedFields.getAllFields()
            .stream()
            .filter(extractedField -> requiredFields.contains(extractedField.getName()) == false)
            .count();
        if (nonRequiredFieldsCount == 0) {
            StringBuilder msgBuilder = new StringBuilder("at least one field must be included in the analysis");