### 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
job.getId(),
            Collections.singletonList("data")
        );
        if (maxEmptySearches != null) {
            datafeedConfigBuilder.setMaxEmptySearches(maxEmptySearches);
        }
        DatafeedConfig datafeedConfig = datafeedConfigBuilder.build();
        putDatafeed(datafeedConfig);
        startDatafeed(datafeedConfig.getId(), 0L, null);
        assertBusy(() -> {
            DataCounts dataCounts = getDataCounts(job.getId());
            assertThat(dataCounts.getProcessedRecordCount(), equalTo(numDocs1));
            assertThat(dataCounts.getOutOfOrderTimeStampCount(), equalTo(0L));
        });
        now = System.currentTimeMillis();
        long numDocs2;
        if (maxEmptySearches == null) {
            numDocs2 = randomIntBetween(2, 64);
            indexDocs(logger, "data", numDocs2, now + 5000, now + 6000);
        } else {
            numDocs2 = 0;
        }
        assertBusy(() -> {
            DataCounts dataCounts = getDataCounts(job.getId());
            assertThat(dataCounts.getProcessedRecordCount(), equalTo(numDocs1 + numDocs2));
            assertThat(dataCounts.getOutOfOrderTimeStampCount(), equalTo(0L));
        }, 30, TimeUnit.SECONDS);
    }
}