### 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
import org.elasticsearch.xpack.core.action.XPackInfoFeatureAction;
import org.elasticsearch.xpack.core.action.XPackUsageFeatureAction;
import org.elasticsearch.xpack.core.searchablesnapshots.MountSearchableSnapshotAction;
import org.elasticsearch.xpack.searchablesnapshots.action.ClearSearchableSnapshotsCacheAction;
import org.elasticsearch.xpack.searchablesnapshots.action.SearchableSnapshotsInfoTransportAction;
import org.elasticsearch.xpack.searchablesnapshots.action.SearchableSnapshotsStatsAction;
import org.elasticsearch.xpack.searchablesnapshots.action.SearchableSnapshotsUsageTransportAction;
import org.elasticsearch.xpack.searchablesnapshots.action.TransportClearSearchableSnapshotsCacheAction;
import org.elasticsearch.xpack.searchablesnapshots.action.TransportMountSearchableSnapshotAction;
import org.elasticsearch.xpack.searchablesnapshots.action.TransportSearchableSnapshotsStatsAction;
import org.elasticsearch.xpack.searchablesnapshots.action.cache.FrozenCacheInfoAction;
import org.elasticsearch.xpack.searchablesnapshots.action.cache.FrozenCacheInfoNodeAction;
import org.elasticsearch.xpack.searchablesnapshots.action.cache.TransportSearchableSnapshotCacheStoresAction;
import org.elasticsearch.xpack.searchablesnapshots.action.cache.TransportSearchableSnapshotsNodeCachesStatsAction;
import org.elasticsearch.xpack.searchablesnapshots.allocation.FailShardsOnInvalidLicenseClusterListener;
import org.elasticsearch.xpack.searchablesnapshots.allocation.SearchableSnapshotAllocator;
import org.elasticsearch.xpack.searchablesnapshots.allocation.SearchableSnapshotIndexEventListener;
import org.elasticsearch.xpack.searchablesnapshots.allocation.SearchableSnapshotIndexFoldersDeletionListener;
import org.elasticsearch.xpack.searchablesnapshots.allocation.decider.DedicatedFrozenNodeAllocationDecider;
import org.elasticsearch.xpack.searchablesnapshots.allocation.decider.HasFrozenCacheAllocationDecider;
import org.elasticsearch.xpack.searchablesnapshots.allocation.decider.SearchableSnapshotAllocationDecider;
import org.elasticsearch.xpack.searchablesnapshots.allocation.decider.SearchableSnapshotEnableAllocationDecider;
import org.elasticsearch.xpack.searchablesnapshots.allocation.decider.SearchableSnapshotRepositoryExistsAllocationDecider;
import org.elasticsearch.xpack.searchablesnapshots.cache.blob.BlobStoreCacheMaintenanceService;
import org.elasticsearch.xpack.searchablesnapshots.cache.blob.BlobStoreCacheService;
import org.elasticsearch.xpack.searchablesnapshots.cache.common.CacheKey;
import org.elasticsearch.xpack.searchablesnapshots.cache.full.CacheService;
import org.elasticsearch.xpack.searchablesnapshots.cache.full.PersistentCache;
import org.elasticsearch.xpack.searchablesnapshots.cache.shared.FrozenCacheInfoService;
import org.elasticsearch.xpack.searchablesnapshots.recovery.SearchableSnapshotRecoveryState;