### 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
);
        assertThat(e.getResponse().getStatusLine().getStatusCode(), equalTo(400));
        assertThat(e.getMessage(), containsString("The job cannot be created with the Id '" + jobId + "'. The Id is already used."));
    }
    public void testCreateJobsWithIndexNameOption() throws Exception {
        String jobTemplate = """
            {
              "analysis_config" : {
                    "detectors" :[{"function":"metric","field_name":"responsetime"}]
                },
              "data_description": {},
              "results_index_name" : "%s"}""";
        String jobId1 = "create-jobs-with-index-name-option-job-1";
        String indexName = "non-default-index";
        putJob(jobId1, String.format(Locale.ROOT, jobTemplate, indexName));
        String jobId2 = "create-jobs-with-index-name-option-job-2";
        putJob(jobId2, String.format(Locale.ROOT, jobTemplate, indexName));
        
        
        
        assertBusy(() -> {
            try {
                String aliasesResponse = getAliases();
                assertThat(aliasesResponse, containsString("""
                    "%s":{"aliases":{""".formatted(AnomalyDetectorsIndex.jobResultsAliasedName("custom-" + indexName))));
                assertThat(
                    aliasesResponse,
                    containsString(
                        """
                            "%s":{"filter":{"term":{"job_id":{"value":"%s"}}},"is_hidden":true}""".formatted(