### Elasticsearch Version

8.8.1+ but probably all versions

### Installed Plugins

_No response_

### Java Version

_bundled_

### OS Version

cloud

### Problem Description

This is a follow-up of [#97370](https://github.com/elastic/elasticsearch/issues/97370). 

In a case where disk spaces are reaching limits, if ILM suddenly tries to move a lot of hot shards to cold/frozen shards, it can tip the cluster health to RED because a lot of cold/frozen shards may be created and stay unassigned as long as there is not enough disk space. However, this is not a suitable indicator for service unavailability, since the data is still safely in the respective hot shards that are becoming cold/frozen, and will remain there until the cold/frozen shards are assigned so that searches can still search them.

Thus the [Health Report API](https://www.elastic.co/guide/en/elasticsearch/reference/8.8/health-api.html) should not return RED for unassigned cold/frozen shards of ILM moves.

### Steps to Reproduce

In a case where disk spaces are reaching limits, if ILM suddenly tries to move a lot of hot shards to cold/frozen shards, it can tip the cluster health to RED because a lot of cold/frozen shards may be created and stay unassigned (as long as there is not enough disk space).

### Logs (if relevant)

_No response_
x-pack/plugin/searchable-snapshots/src/main/java/org/elasticsearch/xpack/searchablesnapshots/SearchableSnapshots.java
.build()
        );
    }
    @Override
    public String getFeatureName() {
        return "searchable_snapshots";
    }
    @Override
    public String getFeatureDescription() {
        return "Manages caches and configuration for searchable snapshots";
    }
    @Override
    public Map<String, DirectoryFactory> getDirectoryFactories() {
        return Map.of(SEARCHABLE_SNAPSHOT_STORE_TYPE, (indexSettings, shardPath) -> {
            final RepositoriesService repositories = repositoriesServiceSupplier.get();
            assert repositories != null;
            final CacheService cache = cacheService.get();
            assert cache != null;
            final ThreadPool threadPool = this.threadPool.get();
            assert threadPool != null;
            final BlobStoreCacheService blobCache = blobStoreCacheService.get();
            assert blobCache != null;
            return SearchableSnapshotDirectory.create(
                repositories,
                cache,
                indexSettings,
                shardPath,
                System::nanoTime,
                threadPool,
                blobCache,