### 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
SNAPSHOT_BLOB_CACHE_METADATA_FILES_MAX_LENGTH,
                    BufferedIndexInput.BUFFER_SIZE
                );
                throw new IllegalArgumentException(message);
            }
        },
        Setting.Property.IndexScope,
        Setting.Property.NotCopyableOnResize
    );
    /**
     * Index setting used to indicate if the snapshot that is mounted as an index should be deleted when the index is deleted. This setting
     * is only set for indices mounted in clusters on or after 8.0.0. Once set this setting cannot be updated.
     */
    public static final Setting<Boolean> DELETE_SEARCHABLE_SNAPSHOT_ON_INDEX_DELETION = Setting.boolSetting(
        SearchableSnapshotsSettings.SEARCHABLE_SNAPSHOTS_DELETE_SNAPSHOT_ON_INDEX_DELETION,
        false,
        Setting.Property.Final,
        Setting.Property.IndexScope,
        Setting.Property.PrivateIndex,
        Setting.Property.NotCopyableOnResize
    );
    /**
     * Prefer to allocate to the data content tier and then the hot tier.
     * This affects the system searchable snapshot cache index (not the searchable snapshot index itself)
     */
    public static final String DATA_TIERS_CACHE_INDEX_PREFERENCE = String.join(",", DataTier.DATA_CONTENT, DataTier.DATA_HOT);
    private static final int SEARCHABLE_SNAPSHOTS_INDEX_MAPPINGS_VERSION = 1;
    private volatile Supplier<RepositoriesService> repositoriesServiceSupplier;
    private final SetOnce<BlobStoreCacheService> blobStoreCacheService = new SetOnce<>();
    private final SetOnce<CacheService> cacheService = new SetOnce<>();