### 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
if (indexModule.indexSettings().getIndexMetadata().isSearchableSnapshot()) {
            indexModule.addIndexEventListener(
                new SearchableSnapshotIndexEventListener(settings, cacheService.get(), frozenCacheService.get())
            );
            indexModule.addIndexEventListener(failShardsListener.get());
            indexModule.addSettingsUpdateConsumer(IndexMetadata.INDEX_BLOCKS_WRITE_SETTING, s -> {}, write -> {
                if (write == false) {
                    throw new IllegalArgumentException("Cannot remove write block from searchable snapshot index");
                }
            });
        }
    }
    @Override
    public List<IndexFoldersDeletionListener> getIndexFoldersDeletionListeners() {
        if (DiscoveryNode.canContainData(settings)) {
            return List.of(new SearchableSnapshotIndexFoldersDeletionListener(cacheService::get, frozenCacheService::get));
        }
        return List.of();
    }
    @Override
    public Collection<SystemIndexDescriptor> getSystemIndexDescriptors(Settings unused) {
        return List.of(
            SystemIndexDescriptor.builder()
                .setIndexPattern(SNAPSHOT_BLOB_CACHE_INDEX_PATTERN)
                .setDescription("Contains cached data of blob store repositories")
                .setPrimaryIndex(SNAPSHOT_BLOB_CACHE_INDEX)
                .setMappings(getIndexMappings())
                .setSettings(getIndexSettings())
                .setOrigin(SEARCHABLE_SNAPSHOTS_ORIGIN)
                .setVersionMetaKey("version")