### 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
StartDataFrameAnalyticsAction.Request,
    NodeAcknowledgedResponse> {
    private static final Logger logger = LogManager.getLogger(TransportStartDataFrameAnalyticsAction.class);
    private static final String PRIMARY_SHARDS_INACTIVE = "not all primary shards are active";
    private final XPackLicenseState licenseState;
    private final Client client;
    private final PersistentTasksService persistentTasksService;
    private final DataFrameAnalyticsConfigProvider configProvider;
    private final MlMemoryTracker memoryTracker;
    private final DataFrameAnalyticsAuditor auditor;
    private final SourceDestValidator sourceDestValidator;
    @Inject
    public TransportStartDataFrameAnalyticsAction(
        TransportService transportService,
        Client client,
        ClusterService clusterService,
        ThreadPool threadPool,
        ActionFilters actionFilters,
        XPackLicenseState licenseState,
        IndexNameExpressionResolver indexNameExpressionResolver,
        PersistentTasksService persistentTasksService,
        DataFrameAnalyticsConfigProvider configProvider,
        MlMemoryTracker memoryTracker,
        DataFrameAnalyticsAuditor auditor
    ) {