### 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
index,
            alias,
            Settings.builder()
                .put(IndexMetadata.SETTING_NUMBER_OF_SHARDS, 1)
                .put(IndexMetadata.SETTING_NUMBER_OF_REPLICAS, 0)
                .put(LifecycleSettings.LIFECYCLE_NAME, policy)
                .putNull(DataTier.TIER_PREFERENCE) 
                .put(RolloverAction.LIFECYCLE_ROLLOVER_ALIAS, alias)
        );
        
        assertBusy(() -> assertThat(getStepKeyForIndex(client(), index).getPhase(), equalTo("warm")), 30, TimeUnit.SECONDS);
        
        assertBusy(
            () -> assertThat(getStepKeyForIndex(client(), index).getName(), equalTo(AllocationRoutedStep.NAME)),
            30,
            TimeUnit.SECONDS
        );
        String indexWithDataWarmRouting = "indexwithdatawarmrouting";
        Settings.Builder settings = Settings.builder()
            .put(IndexMetadata.SETTING_NUMBER_OF_SHARDS, 1)
            .put(IndexMetadata.SETTING_NUMBER_OF_REPLICAS, 0)
            .put(IndexMetadata.INDEX_ROUTING_REQUIRE_GROUP_SETTING.getKey() + "data", "warm");
        createIndex(indexWithDataWarmRouting, settings.build());
        
        updateIndexSettings(indexWithDataWarmRouting, Settings.builder().putNull(DataTier.TIER_PREFERENCE));
        Request migrateRequest = new Request("POST", "_ilm/migrate_to_data_tiers");
        migrateRequest.addParameter("dry_run", "true");
        migrateRequest.setJsonEntity("{\"legacy_template_to_delete\": \"" + templateName + "\", \"node_attribute\": \"data\"}");
        Response migrateDeploymentResponse = client().performRequest(migrateRequest);
        assertOK(migrateDeploymentResponse);