### 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/DatafeedJobsIT.java
assertThat(response.getResponse().results().get(0).getDatafeedState(), equalTo(DatafeedState.STOPPED));
        }, 60, TimeUnit.SECONDS);
        waitUntilJobIsClosed(job.getId());
    }
    public void testLookbackOnlyDataStream() throws Exception {
        String mapping = """
            {
                  "properties": {
                    "time": {
                      "type": "date"
                    },        "@timestamp": {
                      "type": "date"
                    }      }
                }""";
        createDataStreamAndTemplate("datafeed_data_stream", mapping);
        long numDocs = randomIntBetween(32, 2048);
        long now = System.currentTimeMillis();
        long oneWeekAgo = now - 604800000;
        long twoWeeksAgo = oneWeekAgo - 604800000;
        indexDocs(logger, "datafeed_data_stream", numDocs, twoWeeksAgo, oneWeekAgo);
        client().admin().cluster().prepareHealth("datafeed_data_stream").setWaitForYellowStatus().get();
        Job.Builder job = createScheduledJob("lookback-data-stream-job");
        PutJobAction.Response putJobResponse = putJob(job);
        assertThat(putJobResponse.getResponse().getJobVersion(), equalTo(Version.CURRENT));
        openJob(job.getId());
        assertBusy(() -> assertEquals(getJobStats(job.getId()).get(0).getState(), JobState.OPENED));
        DatafeedConfig datafeedConfig = createDatafeed(
            job.getId() + "-datafeed",
            job.getId(),
            Collections.singletonList("datafeed_data_stream")