### 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
"index.store.snapshot.cache.excluded_file_types",
        Setting.Property.IndexScope,
        Setting.Property.NodeScope,
        Setting.Property.NotCopyableOnResize
    );
    public static final Setting<ByteSizeValue> SNAPSHOT_UNCACHED_CHUNK_SIZE_SETTING = Setting.byteSizeSetting(
        "index.store.snapshot.uncached_chunk_size",
        ByteSizeValue.MINUS_ONE,
        Setting.Property.IndexScope,
        Setting.Property.NodeScope,
        Setting.Property.NotCopyableOnResize
    );
    public static final String SNAPSHOT_BLOB_CACHE_INDEX = ".snapshot-blob-cache";
    public static final String SNAPSHOT_BLOB_CACHE_INDEX_PATTERN = SNAPSHOT_BLOB_CACHE_INDEX + "*";
    public static final String SNAPSHOT_BLOB_CACHE_METADATA_FILES_MAX_LENGTH = "index.store.snapshot.blob_cache.metadata_files.max_length";
    public static final Setting<ByteSizeValue> SNAPSHOT_BLOB_CACHE_METADATA_FILES_MAX_LENGTH_SETTING = new Setting<>(
        SNAPSHOT_BLOB_CACHE_METADATA_FILES_MAX_LENGTH,
        new ByteSizeValue(64L, ByteSizeUnit.KB).getStringRep(),
        s -> Setting.parseByteSize(
            s,
            new ByteSizeValue(1L, ByteSizeUnit.KB),
            ByteSizeValue.ofBytes(Long.MAX_VALUE),
            SNAPSHOT_BLOB_CACHE_METADATA_FILES_MAX_LENGTH
        ),
        value -> {
            if (value.getBytes() % BufferedIndexInput.BUFFER_SIZE != 0L) {
                final String message = String.format(
                    Locale.ROOT,
                    "failed to parse value [%s] for setting [%s], must be a multiple of [%s] bytes",
                    value.getStringRep(),