### 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
} catch (Exception e) {
            if (e.getMessage().equals("Cannot start because the job has already finished")) {
                
            } else {
                throw e;
            }
        }
        waitUntilAnalyticsIsStopped(id);
        
        SearchResponse searchResponse = client().prepareSearch(config.getDest().getIndex()).setTrackTotalHits(true).get();
        assertThat(searchResponse.getHits().getTotalHits().value, equalTo((long) docCount));
        
        searchResponse = client().prepareSearch(config.getDest().getIndex())
            .setTrackTotalHits(true)
            .setQuery(QueryBuilders.existsQuery("custom_ml.outlier_score"))
            .get();
        assertThat(searchResponse.getHits().getTotalHits().value, equalTo((long) docCount));
        assertProgressComplete(id);
        assertThat(searchStoredProgress(id).getHits().getTotalHits().value, equalTo(1L));
    }
    public void testOutlierDetectionWithCustomParams() throws Exception {
        String sourceIndex = "test-outlier-detection-with-custom-params";
        client().admin()
            .indices()
            .prepareCreate(sourceIndex)
            .setMapping("numeric_1", "type=double", "numeric_2", "type=float", "categorical_1", "type=keyword")
            .get();
        BulkRequestBuilder bulkRequestBuilder = client().prepareBulk();
        bulkRequestBuilder.setRefreshPolicy(WriteRequest.RefreshPolicy.IMMEDIATE);
        for (int i = 0; i < 5; i++) {