### 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/RunDataFrameAnalyticsIT.java
waitUntilAnalyticsIsFailed(id);
        forceStopAnalytics(id);
        waitUntilAnalyticsIsStopped(id);
    }
    public void testLazyAssignmentWithModelMemoryLimitTooHighForAssignment() throws Exception {
        String sourceIndex = "test-lazy-assign-model-memory-limit-too-high";
        client().admin()
            .indices()
            .prepareCreate(sourceIndex)
            .setMapping("col_1", "type=double", "col_2", "type=float", "col_3", "type=keyword")
            .get();
        BulkRequestBuilder bulkRequestBuilder = client().prepareBulk().setRefreshPolicy(WriteRequest.RefreshPolicy.IMMEDIATE);
        IndexRequest indexRequest = new IndexRequest(sourceIndex).id("doc_1").source("col_1", 1.0, "col_2", 1.0, "col_3", "str");
        bulkRequestBuilder.add(indexRequest);
        BulkResponse bulkResponse = bulkRequestBuilder.get();
        if (bulkResponse.hasFailures()) {
            fail("Failed to index data: " + bulkResponse.buildFailureMessage());
        }
        String id = "test_lazy_assign_model_memory_limit_too_high";
        
        ByteSizeValue modelMemoryLimit = ByteSizeValue.ofTb(1);
        DataFrameAnalyticsConfig config = new DataFrameAnalyticsConfig.Builder().setId(id)
            .setSource(new DataFrameAnalyticsSource(new String[] { sourceIndex }, null, null, null))
            .setDest(new DataFrameAnalyticsDest(sourceIndex + "-results", null))
            .setAnalysis(new OutlierDetection.Builder().build())
            .setModelMemoryLimit(modelMemoryLimit)
            .setAllowLazyStart(true)
            .build();
        putAnalytics(config);
        assertIsStopped(id);