### 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
ResponseException e = expectThrows(
            ResponseException.class,
            () -> putJob(jobId2, String.format(Locale.ROOT, jobTemplate, byFieldName2))
        );
        assertThat(
            e.getMessage(),
            containsString(
                "This job would cause a mapping clash with existing field [response] - "
                    + "avoid the clash by assigning a dedicated results index"
            )
        );
    }
    public void testOpenJobFailsWhenPersistentTaskAssignmentDisabled() throws Exception {
        String jobId = "open-job-with-persistent-task-assignment-disabled";
        createFarequoteJob(jobId);
        Request disablePersistentTaskAssignmentRequest = new Request("PUT", "_cluster/settings");
        disablePersistentTaskAssignmentRequest.setJsonEntity("""
            {
              "persistent": {
                "cluster.persistent_tasks.allocation.enable": "none"
              }
            }""");
        Response disablePersistentTaskAssignmentResponse = client().performRequest(disablePersistentTaskAssignmentRequest);
        assertThat(entityAsMap(disablePersistentTaskAssignmentResponse), hasEntry("acknowledged", true));
        try {
            ResponseException exception = expectThrows(ResponseException.class, () -> openJob(jobId));
            assertThat(exception.getResponse().getStatusLine().getStatusCode(), equalTo(429));
            assertThat(
                EntityUtils.toString(exception.getResponse().getEntity()),
                containsString(