### 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/MlJobIT.java
private static final String BASIC_AUTH_VALUE = UsernamePasswordToken.basicAuthHeaderValue(
        "x_pack_rest_user",
        SecuritySettingsSourceField.TEST_PASSWORD_SECURE_STRING
    );
    private static final RequestOptions POST_DATA = RequestOptions.DEFAULT.toBuilder()
        .setWarningsHandler(
            warnings -> Collections.singletonList(
                "Posting data directly to anomaly detection jobs is deprecated, "
                    + "in a future major version it will be compulsory to use a datafeed"
            ).equals(warnings) == false
        )
        .build();
    @Override
    protected Settings restClientSettings() {
        return Settings.builder().put(super.restClientSettings()).put(ThreadContext.PREFIX + ".Authorization", BASIC_AUTH_VALUE).build();
    }
    @Override
    protected boolean preserveTemplatesUponCompletion() {
        return true;
    }
    public void testPutJob_GivenFarequoteConfig() throws Exception {
        Response response = createFarequoteJob("given-farequote-config-job");
        String responseAsString = EntityUtils.toString(response.getEntity());
        assertThat(responseAsString, containsString("\"job_id\":\"given-farequote-config-job\""));
    }
    public void testGetJob_GivenNoSuchJob() {
        ResponseException e = expectThrows(
            ResponseException.class,
            () -> client().performRequest(new Request("GET", MachineLearning.BASE_PATH + "anomaly_detectors/non-existing-job/_stats"))