### 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
Settings indexSettings = Settings.builder()
                .put("index.number_of_shards", 1)
                .put("index.routing.allocation.require.data", "hot")
                .build();
            legacyTemplateToMigrateReq.setJsonEntity(
                "{\"index_patterns\":  [\"legacynotreallyimportant-*\"], \"settings\":  " + Strings.toString(indexSettings) + "}"
            );
            legacyTemplateToMigrateReq.setOptions(
                expectWarnings("Legacy index templates are deprecated in favor of composable templates" + ".")
            );
            assertOK(client().performRequest(legacyTemplateToMigrateReq));
        }
        
        String legacyTemplate = "legacy_template";
        {
            Request legacyTemplateRequest = new Request("PUT", "/_template/" + legacyTemplate);
            Settings indexSettings = Settings.builder().put("index.number_of_shards", 1).build();
            legacyTemplateRequest.setJsonEntity(
                "{\"index_patterns\":  [\"legacynotreallyimportant-*\"], \"settings\":  " + Strings.toString(indexSettings) + "}"
            );
            legacyTemplateRequest.setOptions(expectWarnings("Legacy index templates are deprecated in favor of composable templates."));
            assertOK(client().performRequest(legacyTemplateRequest));
        }
        
        String composableTemplateToMigrate = "to_migrate_composable_template";
        {
            Request toMigrateComposableTemplateReq = new Request("PUT", "/_index_template/" + composableTemplateToMigrate);
            Settings indexSettings = Settings.builder()
                .put("index.number_of_shards", 1)
                .put("index.routing.allocation.require.data", "hot")