### 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
}
    /**
     * Refreshed the cached ILM phase definition for the indices managed by the migrated policy.
     */
    static void refreshCachedPhases(
        Metadata.Builder mb,
        ClusterState currentState,
        LifecyclePolicyMetadata oldPolicyMetadata,
        LifecyclePolicyMetadata newPolicyMetadata,
        NamedXContentRegistry xContentRegistry,
        Client client,
        XPackLicenseState licenseState
    ) {
        
        
        updateIndicesForPolicy(mb, currentState, xContentRegistry, client, oldPolicyMetadata.getPolicy(), newPolicyMetadata, licenseState);
        LifecyclePolicy newLifecyclePolicy = newPolicyMetadata.getPolicy();
        List<String> migratedPhasesWithoutAllocateAction = getMigratedPhasesWithoutAllocateAction(
            oldPolicyMetadata.getPolicy(),
            newLifecyclePolicy
        );
        if (migratedPhasesWithoutAllocateAction.size() > 0) {
            logger.debug(
                "the updated policy [{}] does not contain the allocate action in phases [{}] anymore",
                newLifecyclePolicy.getName(),
                migratedPhasesWithoutAllocateAction
            );