### 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
*/
    static List<String> migrateIndices(Metadata.Builder mb, ClusterState currentState, String nodeAttrName) {
        List<String> migratedIndices = new ArrayList<>();
        String nodeAttrIndexRequireRoutingSetting = INDEX_ROUTING_REQUIRE_GROUP_SETTING.getKey() + nodeAttrName;
        String nodeAttrIndexIncludeRoutingSetting = INDEX_ROUTING_INCLUDE_GROUP_SETTING.getKey() + nodeAttrName;
        String nodeAttrIndexExcludeRoutingSetting = INDEX_ROUTING_EXCLUDE_GROUP_SETTING.getKey() + nodeAttrName;
        for (var indexMetadata : currentState.metadata().indices().values()) {
            String indexName = indexMetadata.getIndex().getName();
            Settings currentSettings = indexMetadata.getSettings();
            boolean removeNodeAttrIndexRoutingSettings = true;
            
            Settings newSettings = maybeMigrateRoutingSettingToTierPreference(
                nodeAttrIndexRequireRoutingSetting,
                currentSettings,
                indexName
            );
            
            
            newSettings = maybeMigrateRoutingSettingToTierPreference(nodeAttrIndexIncludeRoutingSetting, newSettings, indexName);
            if (newSettings.equals(currentSettings)) {
                removeNodeAttrIndexRoutingSettings = false;
                
                
                newSettings = migrateToDefaultTierPreference(currentState, indexMetadata);
            }
            if (newSettings.equals(currentSettings) == false) {
                Settings.Builder finalSettings = Settings.builder().put(newSettings);
                if (removeNodeAttrIndexRoutingSettings) {