### 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
*  We are only able to convert the `frozen`, `cold`, `warm`, or `hot` setting values to the `_tier_preference`. If other
     *  configuration values are present eg ("the_warm_nodes") the index will not be migrated.
     *  If the require or include setting is successfully migrated to _tier_preference, all the **other** routing settings for the
     *  provided attribute are also removed (if present).
     *  Eg. if we manage to migrate the `index.routing.allocation.require.data` setting, but the index also has configured
     *  `index.routing.allocation.include.data` and `index.routing.allocation.exclude.data`, the
     *  migrated settings will contain `index.routing.allocation.include._tier_preference` configured to the corresponding
     *  `index.routing.allocation.require.data` value, with `index.routing.allocation.include.data` and
     *  `index.routing.allocation.exclude.data` being removed.
     *  Settings:
     *    {
     *      index.routing.allocation.require.data: "warm",
     *      index.routing.allocation.include.data: "rack1",
     *      index.routing.allocation.exclude.data: "rack2,rack3"
     *    }
     *  will be migrated to:
     *    {
     *        index.routing.allocation.include._tier_preference: "data_warm,data_hot"
     *    }
     *
     * If both the `index.routing.allocation.require.data` and `index.routing.allocation.include.data` settings are configured to
     * recognized values the coldest one will be converted to the corresponding `_tier_preference` configuration.
     * Eg. the following configuration:
     *    {
     *      index.routing.allocation.require.data: "warm",
     *      index.routing.allocation.include.data: "cold",
     *      index.routing.allocation.exclude.data: "rack2,rack3"
     *    }
     *  will be migrated to:
     *    {