### Elasticsearch Version

7.17, 8.x

### Installed Plugins

_No response_

### Java Version

_bundled_

### OS Version

Darwin

### Problem Description

The migrate to data tiers routing API changes the allocation configuration for 
the indices that need migrating to data tiers routing. 
After such changes we should do a cluster re-route so the allocation changes
take effect immediately. 

### Steps to Reproduce

1. On a one node `data_hot,data_content,master` node create the following index
```
PUT datatiers_problem_index
{
    "settings": {
        "index.routing.allocation.include._tier_preference": "data_hot",
        "index.routing.allocation.require.data": "hot"
    }
}
```
2. Migrate to data tiers and observe the shard is not allocated afterwards
`POST _ilm/migrate_to_data_tiers`

### Logs (if relevant)

_No response_
x-pack/plugin/ilm/qa/multi-node/src/javaRestTest/java/org/elasticsearch/xpack/MigrateToDataTiersIT.java
import org.elasticsearch.xpack.core.ilm.LifecycleSettings;
import org.elasticsearch.xpack.core.ilm.OperationMode;
import org.elasticsearch.xpack.core.ilm.Phase;
import org.elasticsearch.xpack.core.ilm.RolloverAction;
import org.elasticsearch.xpack.core.ilm.SetPriorityAction;
import org.elasticsearch.xpack.core.ilm.ShrinkAction;
import org.junit.AfterClass;
import org.junit.Before;
import java.io.IOException;
import java.util.HashMap;
import java.util.List;
import java.util.Locale;
import java.util.Map;
import java.util.concurrent.TimeUnit;
import static java.util.Collections.singletonMap;
import static org.elasticsearch.xpack.TimeSeriesRestDriver.createIndexWithSettings;
import static org.elasticsearch.xpack.TimeSeriesRestDriver.createNewSingletonPolicy;
import static org.elasticsearch.xpack.TimeSeriesRestDriver.createPolicy;
import static org.elasticsearch.xpack.TimeSeriesRestDriver.getOnlyIndexSettings;
import static org.elasticsearch.xpack.TimeSeriesRestDriver.getStepKeyForIndex;
import static org.hamcrest.Matchers.anEmptyMap;
import static org.hamcrest.Matchers.contains;
import static org.hamcrest.Matchers.containsInAnyOrder;
import static org.hamcrest.Matchers.containsString;
import static org.hamcrest.Matchers.equalTo;
import static org.hamcrest.Matchers.is;
import static org.hamcrest.Matchers.not;
import static org.hamcrest.Matchers.notNullValue;
import static org.hamcrest.Matchers.nullValue;
public class MigrateToDataTiersIT extends ESRestTestCase {