### 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
/*
 * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
 * or more contributor license agreements. Licensed under the Elastic License
 * 2.0; you may not use this file except in compliance with the Elastic License
 * 2.0.
 */
package org.elasticsearch.xpack;
import org.apache.http.entity.ContentType;
import org.apache.http.entity.StringEntity;
import org.apache.http.util.EntityUtils;
import org.elasticsearch.client.Request;
import org.elasticsearch.client.Response;
import org.elasticsearch.client.ResponseException;
import org.elasticsearch.cluster.metadata.IndexMetadata;
import org.elasticsearch.cluster.routing.allocation.DataTier;
import org.elasticsearch.common.Strings;
import org.elasticsearch.common.settings.Settings;
import org.elasticsearch.core.Booleans;
import org.elasticsearch.core.TimeValue;
import org.elasticsearch.rest.RestStatus;
import org.elasticsearch.rest.action.admin.indices.RestPutIndexTemplateAction;
import org.elasticsearch.test.XContentTestUtils;
import org.elasticsearch.test.XContentTestUtils.JsonMapView;
import org.elasticsearch.test.rest.ESRestTestCase;
import org.elasticsearch.xpack.cluster.action.MigrateToDataTiersResponse;
import org.elasticsearch.xpack.core.ilm.AllocateAction;
import org.elasticsearch.xpack.core.ilm.AllocationRoutedStep;
import org.elasticsearch.xpack.core.ilm.DeleteAction;
import org.elasticsearch.xpack.core.ilm.ForceMergeAction;
import org.elasticsearch.xpack.core.ilm.LifecycleAction;