### 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/src/main/java/org/elasticsearch/xpack/ilm/action/TransportMigrateToDataTiersAction.java
private final NamedXContentRegistry xContentRegistry;
    private final Client client;
    private final XPackLicenseState licenseState;
    @Inject
    public TransportMigrateToDataTiersAction(
        TransportService transportService,
        ClusterService clusterService,
        ThreadPool threadPool,
        ActionFilters actionFilters,
        IndexNameExpressionResolver indexNameExpressionResolver,
        NamedXContentRegistry xContentRegistry,
        Client client,
        XPackLicenseState licenseState
    ) {
        super(
            MigrateToDataTiersAction.NAME,
            transportService,
            clusterService,
            threadPool,
            actionFilters,
            MigrateToDataTiersRequest::new,
            indexNameExpressionResolver,
            MigrateToDataTiersResponse::new,
            ThreadPool.Names.SAME
        );
        this.xContentRegistry = xContentRegistry;
        this.client = client;