### Elasticsearch Version

7.17, 8.x

### Installed Plugins

_No response_

### Java Version

_bundled_

### OS Version

Darwin

### Problem Description

The migrate to data tiers API can sometimes configure an illegal value for the `_tier_preference` setting for partially mounted indices.
This can happen if two conditions are met: 
1. if the partially mounted index doesn't have a `_tier_preference` configured
2. if the migrate to data tiers API doesn't perform any migration for this index (e.g. say this partially mounted index doesn't use the `data` custom attribute name for any allocation filtering, but either uses some other node attribute name or none at all)

In this case this piece of code kicks in to configure a default tier preference https://github.com/elastic/elasticsearch/blob/main/x-pack/plugin/ilm/src/main/java/org/elasticsearch/xpack/cluster/metadata/MetadataMigrateToDataTiersRoutingService.java#L534

This is wrong, and we should configure the `MountSearchableSnapshotRequest.Storage.defaultDataTiersPreference` as the tier preference.

Relates to https://github.com/elastic/elasticsearch/issues/84758

### Steps to Reproduce

1. Mount an index - `partial-test`
2. Remove the `_tier_preference` using
```
PUT partial-test/_settings
{
  "index.routing.allocation.include._tier_preference": null
}
```
3. Call the migrate to data tiers routing API 
```
POST /_ilm/migrate_to_data_tiers
```

### Logs (if relevant)

_No response_
x-pack/plugin/ilm/src/main/java/org/elasticsearch/xpack/cluster/metadata/MetadataMigrateToDataTiersRoutingService.java
import org.elasticsearch.xpack.core.ilm.LifecycleAction;
import org.elasticsearch.xpack.core.ilm.LifecyclePolicy;
import org.elasticsearch.xpack.core.ilm.LifecyclePolicyMetadata;
import org.elasticsearch.xpack.core.ilm.MigrateAction;
import org.elasticsearch.xpack.core.ilm.Phase;
import org.elasticsearch.xpack.core.ilm.PhaseExecutionInfo;
import org.elasticsearch.xpack.core.ilm.Step;
import java.time.Instant;
import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Objects;
import java.util.SortedMap;
import java.util.TreeMap;
import static org.elasticsearch.cluster.metadata.IndexMetadata.INDEX_ROUTING_EXCLUDE_GROUP_SETTING;
import static org.elasticsearch.cluster.metadata.IndexMetadata.INDEX_ROUTING_INCLUDE_GROUP_SETTING;
import static org.elasticsearch.cluster.metadata.IndexMetadata.INDEX_ROUTING_REQUIRE_GROUP_SETTING;
import static org.elasticsearch.cluster.metadata.LifecycleExecutionState.ILM_CUSTOM_METADATA_KEY;
import static org.elasticsearch.cluster.routing.allocation.DataTier.ENFORCE_DEFAULT_TIER_PREFERENCE;
import static org.elasticsearch.cluster.routing.allocation.DataTier.TIER_PREFERENCE;
import static org.elasticsearch.xpack.core.ilm.LifecycleOperationMetadata.currentILMMode;
import static org.elasticsearch.xpack.core.ilm.OperationMode.STOPPED;
import static org.elasticsearch.xpack.core.ilm.PhaseCacheManagement.updateIndicesForPolicy;
import static org.elasticsearch.xpack.ilm.IndexLifecycleTransition.moveStateToNextActionAndUpdateCachedPhase;
/**
 * Exposes the necessary methods to migrate a system's elasticsearch abstractions to use data tiers for index allocation routing.
 */
public final class MetadataMigrateToDataTiersRoutingService {