### 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
MlIndexAndAlias.createSystemIndexIfNecessary(
                client,
                clusterState,
                MachineLearning.getInferenceIndexSystemIndexDescriptor(),
                MlTasks.PERSISTENT_TASK_MASTER_NODE_TIMEOUT,
                indexCheckListener
            );
        }
        private void executeTask(DataFrameAnalyticsTask task) {
            DataFrameAnalyticsTaskState startedState = new DataFrameAnalyticsTaskState(
                DataFrameAnalyticsState.STARTED,
                task.getAllocationId(),
                null
            );
            task.updatePersistentTaskState(
                startedState,
                ActionListener.wrap(
                    response -> manager.execute(task, clusterState, MlTasks.PERSISTENT_TASK_MASTER_NODE_TIMEOUT),
                    task::markAsFailed
                )
            );
        }
        public static String nodeFilter(DiscoveryNode node, TaskParams params) {
            String id = params.getId();
            if (node.getVersion().before(TaskParams.VERSION_INTRODUCED)) {
                return "Not opening job ["
                    + id
                    + "] on node ["
                    + JobNodeSelector.nodeNameAndVersion(node)