### 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
attribute = DEFAULT_NODE_ATTRIBUTE_NAME;
        }
        List<String> migratedPolicies = migrateIlmPolicies(mb, currentState, attribute, xContentRegistry, client, licenseState);
        
        
        
        ClusterState intermediateState = ClusterState.builder(currentState).metadata(mb).build();
        mb = Metadata.builder(intermediateState.metadata());
        List<String> migratedIndices = migrateIndices(mb, intermediateState, attribute);
        MigratedTemplates migratedTemplates = migrateIndexAndComponentTemplates(mb, intermediateState, attribute);
        return Tuple.tuple(
            ClusterState.builder(currentState).metadata(mb).build(),
            new MigratedEntities(removedIndexTemplateName, migratedIndices, migratedPolicies, migratedTemplates)
        );
    }
    /**
     * Iterate through the existing ILM policies and look at the configured {@link AllocateAction}s. If they define *any* routing rules
     * based on the provided node attribute name (we look at include, exclude, and require rules) *ALL* the rules in the allocate
     * action will be removed. All the rules are removed in order to allow for ILM to inject the {@link MigrateAction}.
     * This also iterates through all the indices that are executing a given *migrated* policy and refreshes the cached phase definition
     * for each of these managed indices.
     */
    static List<String> migrateIlmPolicies(
        Metadata.Builder mb,
        ClusterState currentState,
        String nodeAttrName,
        NamedXContentRegistry xContentRegistry,
        Client client,
        XPackLicenseState licenseState
    ) {