### 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
/**
     * Stopping a lookback closes the associated job _after_ the stop call returns.
     * This test ensures that a kill request submitted during this close doesn't
     * put the job into the "failed" state.
     */
    public void testStopLookbackFollowedByProcessKill() throws Exception {
        client().admin().indices().prepareCreate("data").setMapping("time", "type=date").get();
        long numDocs = randomIntBetween(1024, 2048);
        long now = System.currentTimeMillis();
        long oneWeekAgo = now - 604800000;
        long twoWeeksAgo = oneWeekAgo - 604800000;
        indexDocs(logger, "data", numDocs, twoWeeksAgo, oneWeekAgo);
        Job.Builder job = createScheduledJob("lookback-job-stopped-then-killed");
        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));
        List<String> t = Collections.singletonList("data");
        DatafeedConfig.Builder datafeedConfigBuilder = createDatafeedBuilder(job.getId() + "-datafeed", job.getId(), t);
        
        datafeedConfigBuilder.setChunkingConfig(ChunkingConfig.newManual(new TimeValue(1, TimeUnit.SECONDS)));
        DatafeedConfig datafeedConfig = datafeedConfigBuilder.build();
        putDatafeed(datafeedConfig);
        startDatafeed(datafeedConfig.getId(), 0L, now);
        assertBusy(() -> {
            DataCounts dataCounts = getDataCounts(job.getId());
            assertThat(dataCounts.getProcessedRecordCount(), greaterThan(0L));
        }, 60, TimeUnit.SECONDS);
        stopDatafeed(datafeedConfig.getId());