### 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
logger.debug(
                            "ILM policy [{}], phase [{}]: removed the deactivated migrate action",
                            lifecyclePolicy.getName(),
                            phase.getName()
                        );
                    }
                }
                Phase updatedPhase = new Phase(phase.getName(), phase.getMinimumAge(), actionMap);
                Map<String, Phase> updatedPhases = new HashMap<>(
                    newLifecyclePolicy == null ? lifecyclePolicy.getPhases() : newLifecyclePolicy.getPhases()
                );
                updatedPhases.put(phaseEntry.getKey(), updatedPhase);
                newLifecyclePolicy = new LifecyclePolicy(lifecyclePolicy.getName(), updatedPhases);
            }
        }
        return newLifecyclePolicy;
    }
    /**
     * Returns true of the provided {@link AllocateAction} defines any index allocation rules.
     */
    static boolean allocateActionDefinesRoutingRules(String nodeAttrName, @Nullable AllocateAction allocateAction) {
        return allocateAction != null
            && (allocateAction.getRequire().get(nodeAttrName) != null
                || allocateAction.getInclude().get(nodeAttrName) != null
                || allocateAction.getExclude().get(nodeAttrName) != null);
    }
    /**
     * Iterates through the existing indices and migrates them away from using attribute based routing using the provided node
     * attribute name towards the tier preference routing.
     * Returns a list of the migrated indices.