### 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/qa/native-multi-node-tests/src/javaRestTest/java/org/elasticsearch/xpack/ml/integration/RunDataFrameAnalyticsIT.java
DataFrameAnalyticsConfig config = buildAnalytics(id, sourceIndex, destIndex, null, new OutlierDetection.Builder().build());
        putAnalytics(config);
        assertIsStopped(id);
        assertProgressIsZero(id);
        startAnalytics(id);
        waitUntilAnalyticsIsStopped(id);
        
        SearchResponse searchResponse = client().prepareSearch(config.getDest().getIndex()).setTrackTotalHits(true).get();
        assertThat(searchResponse.getHits().getTotalHits().value, equalTo((long) bulkRequestBuilder.numberOfActions()));
        
        searchResponse = client().prepareSearch(config.getDest().getIndex())
            .setTrackTotalHits(true)
            .setQuery(QueryBuilders.existsQuery("ml.outlier_score"))
            .get();
        assertThat(searchResponse.getHits().getTotalHits().value, equalTo((long) bulkRequestBuilder.numberOfActions()));
        assertProgressComplete(id);
        assertThat(searchStoredProgress(id).getHits().getTotalHits().value, equalTo(1L));
        assertThatAuditMessagesMatch(
            id,
            "Created analytics with type [outlier_detection]",
            "Estimated memory usage [",
            "Starting analytics on node",
            "Started analytics",
            "Using existing destination index [test-outlier-detection-with-pre-existing-dest-index-results]",
            "Started reindexing to destination index [test-outlier-detection-with-pre-existing-dest-index-results]",
            "Finished reindexing to destination index [test-outlier-detection-with-pre-existing-dest-index-results]",
            "Started loading data",
            "Started analyzing",
            "Started writing results",
            "Finished analysis"