### 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
settings,
                clusterService,
                memoryTracker,
                resolver
            );
            this.client = Objects.requireNonNull(client);
            this.manager = Objects.requireNonNull(manager);
            this.auditor = Objects.requireNonNull(auditor);
            this.licenseState = licenseState;
            clusterService.addListener(event -> clusterState = event.state());
        }
        @Override
        protected AllocatedPersistentTask createTask(
            long id,
            String type,
            String action,
            TaskId parentTaskId,
            PersistentTasksCustomMetadata.PersistentTask<TaskParams> persistentTask,
            Map<String, String> headers
        ) {
            return new DataFrameAnalyticsTask(
                id,
                type,
                action,
                parentTaskId,
                headers,
                client,
                manager,
                auditor,
                persistentTask.getParams(),