### 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_
server/src/main/java/org/elasticsearch/cluster/routing/allocation/DataTier.java
if (dataStreamName != null) {
                        return DATA_HOT_TIER_PREFERENCE_SETTINGS;
                    } else {
                        return DATA_CONTENT_TIER_PREFERENCE_SETTINGS;
                    }
                }
        }
    }
    
    static final class DataTierSettingValidator implements Setting.Validator<String> {
        private static final Collection<Setting<?>> dependencies = List.of(
            IndexModule.INDEX_STORE_TYPE_SETTING,
            SearchableSnapshotsSettings.SNAPSHOT_PARTIAL_SETTING
        );
        public static String getDefaultTierPreference(Settings settings) {
            if (SearchableSnapshotsSettings.isPartialSearchableSnapshotIndex(settings)) {
                return DATA_FROZEN;
            } else {
                return "";
            }
        }
        @Override
        public void validate(String value) {
            if (Strings.hasText(value)) {
                for (String s : parseTierList(value)) {
                    if (validTierName(s) == false) {
                        throw new IllegalArgumentException(
                            "invalid tier names found in [" + value + "] allowed values are " + ALL_DATA_TIERS
                        );
                    }