### 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
return List.of(
            SNAPSHOT_REPOSITORY_UUID_SETTING,
            SNAPSHOT_REPOSITORY_NAME_SETTING,
            SNAPSHOT_SNAPSHOT_NAME_SETTING,
            SNAPSHOT_SNAPSHOT_ID_SETTING,
            SNAPSHOT_INDEX_NAME_SETTING,
            SNAPSHOT_INDEX_ID_SETTING,
            SNAPSHOT_CACHE_ENABLED_SETTING,
            SNAPSHOT_CACHE_PREWARM_ENABLED_SETTING,
            SNAPSHOT_CACHE_EXCLUDED_FILE_TYPES_SETTING,
            SNAPSHOT_UNCACHED_CHUNK_SIZE_SETTING,
            DELETE_SEARCHABLE_SNAPSHOT_ON_INDEX_DELETION,
            SearchableSnapshotsSettings.SNAPSHOT_PARTIAL_SETTING,
            SNAPSHOT_BLOB_CACHE_METADATA_FILES_MAX_LENGTH_SETTING,
            CacheService.SNAPSHOT_CACHE_RANGE_SIZE_SETTING,
            CacheService.SNAPSHOT_CACHE_RECOVERY_RANGE_SIZE_SETTING,
            CacheService.SNAPSHOT_CACHE_SYNC_INTERVAL_SETTING,
            CacheService.SNAPSHOT_CACHE_MAX_FILES_TO_SYNC_AT_ONCE_SETTING,
            CacheService.SNAPSHOT_CACHE_SYNC_SHUTDOWN_TIMEOUT,
            SearchableSnapshotEnableAllocationDecider.SEARCHABLE_SNAPSHOTS_ALLOCATE_ON_ROLLING_RESTART,
            BlobStoreCacheMaintenanceService.SNAPSHOT_SNAPSHOT_CLEANUP_INTERVAL_SETTING,
            BlobStoreCacheMaintenanceService.SNAPSHOT_SNAPSHOT_CLEANUP_KEEP_ALIVE_SETTING,
            BlobStoreCacheMaintenanceService.SNAPSHOT_SNAPSHOT_CLEANUP_BATCH_SIZE_SETTING,
            BlobStoreCacheMaintenanceService.SNAPSHOT_SNAPSHOT_CLEANUP_RETENTION_PERIOD
        );
    }
    @Override
    public Collection<Object> createComponents(
        final Client client,
        final ClusterService clusterService,