### 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
assertIsStopped(id);
        startAnalytics(id);
        
        assertThat(stopAnalytics(id).isStopped(), is(true));
        assertIsStopped(id);
        if (indexExists(config.getDest().getIndex()) == false) {
            
            return;
        }
        SearchResponse searchResponse = client().prepareSearch(config.getDest().getIndex()).setTrackTotalHits(true).get();
        if (searchResponse.getHits().getTotalHits().value == docCount) {
            searchResponse = client().prepareSearch(config.getDest().getIndex())
                .setTrackTotalHits(true)
                .setQuery(QueryBuilders.existsQuery("custom_ml.outlier_score"))
                .get();
            logger.debug("We stopped during analysis: [{}] < [{}]", searchResponse.getHits().getTotalHits().value, docCount);
            assertThat(searchResponse.getHits().getTotalHits().value, lessThan((long) docCount));
        } else {
            logger.debug("We stopped during reindexing: [{}] < [{}]", searchResponse.getHits().getTotalHits().value, docCount);
        }
        assertThatAuditMessagesMatch(
            id,
            "Created analytics with type [outlier_detection]",
            "Estimated memory usage [",
            "Starting analytics on node",
            "Started analytics",
            "Creating destination index [test-stop-outlier-detection-with-enough-docs-to-scroll-results]",
            "Stopped analytics"
        );
    }