### 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
Settings unused,
        RestController restController,
        ClusterSettings clusterSettings,
        IndexScopedSettings indexScopedSettings,
        SettingsFilter settingsFilter,
        IndexNameExpressionResolver indexNameExpressionResolver,
        Supplier<DiscoveryNodes> nodesInCluster
    ) {
        return List.of(
            new RestSearchableSnapshotsStatsAction(),
            new RestClearSearchableSnapshotsCacheAction(),
            new RestMountSearchableSnapshotAction(),
            new RestSearchableSnapshotsNodeCachesStatsAction()
        );
    }
    @Override
    public Map<String, ExistingShardsAllocator> getExistingShardsAllocators() {
        return Map.of(SearchableSnapshotAllocator.ALLOCATOR_NAME, allocator.get());
    }
    
    protected XPackLicenseState getLicenseState() {
        return XPackPlugin.getSharedLicenseState();
    }
    @Override
    public Collection<AllocationDecider> createAllocationDeciders(Settings settingsToUse, ClusterSettings clusterSettings) {
        return List.of(
            new SearchableSnapshotAllocationDecider(() -> SEARCHABLE_SNAPSHOT_FEATURE.checkWithoutTracking(getLicenseState())),
            new SearchableSnapshotRepositoryExistsAllocationDecider(),
            new SearchableSnapshotEnableAllocationDecider(settingsToUse, clusterSettings),
            new HasFrozenCacheAllocationDecider(frozenCacheInfoService),