### 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
client().admin().indices().prepareCreate("data").setMapping("time", "type=date").get();
        long numDocs = randomIntBetween(32, 2048);
        Instant now = Instant.now();
        indexDocs(logger, "data", numDocs, now.minus(Duration.ofDays(14)).toEpochMilli(), now.toEpochMilli());
        Job.Builder job = createScheduledJob("lookback-job-datafeed-recreated");
        String datafeedId = "lookback-datafeed-datafeed-recreated";
        DatafeedConfig datafeedConfig = createDatafeed(datafeedId, job.getId(), Collections.singletonList("data"));
        putJob(job);
        CheckedRunnable<Exception> openAndRunJob = () -> {
            openJob(job.getId());
            assertBusy(() -> assertEquals(getJobStats(job.getId()).get(0).getState(), JobState.OPENED));
            putDatafeed(datafeedConfig);
            
            assertDatafeedStats(datafeedId, DatafeedState.STOPPED, job.getId(), equalTo(0L));
            startDatafeed(datafeedId, 0L, now.toEpochMilli());
            assertBusy(() -> {
                assertThat(getDataCounts(job.getId()).getProcessedRecordCount(), equalTo(numDocs));
                
                assertDatafeedStats(datafeedId, DatafeedState.STOPPED, job.getId(), greaterThan(0L));
            }, 60, TimeUnit.SECONDS);
            deleteDatafeed(datafeedId);
            waitUntilJobIsClosed(job.getId());
        };
        openAndRunJob.run();
        openAndRunJob.run();
    }
    public void testDatafeedTimingStats_QueryDelayUpdated_TimingStatsNotReset() throws Exception {
        client().admin().indices().prepareCreate("data").setMapping("time", "type=date").get();
        long numDocs = randomIntBetween(32, 2048);
        Instant now = Instant.now();