### 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_
server/src/main/java/org/elasticsearch/cluster/routing/allocation/ShardsAvailabilityHealthIndicatorService.java
import static java.util.stream.Collectors.joining;
import static java.util.stream.Collectors.toMap;
import static java.util.stream.Collectors.toSet;
import static org.elasticsearch.cluster.health.ClusterShardHealth.getInactivePrimaryHealth;
import static org.elasticsearch.cluster.metadata.IndexMetadata.INDEX_ROUTING_INCLUDE_GROUP_PREFIX;
import static org.elasticsearch.cluster.metadata.IndexMetadata.INDEX_ROUTING_INCLUDE_GROUP_SETTING;
import static org.elasticsearch.cluster.metadata.IndexMetadata.INDEX_ROUTING_REQUIRE_GROUP_PREFIX;
import static org.elasticsearch.cluster.metadata.IndexMetadata.INDEX_ROUTING_REQUIRE_GROUP_SETTING;
import static org.elasticsearch.cluster.routing.allocation.decider.EnableAllocationDecider.INDEX_ROUTING_ALLOCATION_ENABLE_SETTING;
import static org.elasticsearch.cluster.routing.allocation.decider.ShardsLimitAllocationDecider.CLUSTER_TOTAL_SHARDS_PER_NODE_SETTING;
import static org.elasticsearch.cluster.routing.allocation.decider.ShardsLimitAllocationDecider.INDEX_TOTAL_SHARDS_PER_NODE_SETTING;
import static org.elasticsearch.health.Diagnosis.Resource.Type.FEATURE_STATE;
import static org.elasticsearch.health.Diagnosis.Resource.Type.INDEX;
import static org.elasticsearch.health.HealthStatus.GREEN;
import static org.elasticsearch.health.HealthStatus.RED;
import static org.elasticsearch.health.HealthStatus.YELLOW;
import static org.elasticsearch.health.node.HealthIndicatorDisplayValues.getTruncatedIndices;
import static org.elasticsearch.health.node.HealthIndicatorDisplayValues.indicesComparatorByPriorityAndName;
/**
 * This indicator reports health for shards.
 * <p>
 * Indicator will report:
 * * RED when one or more primary shards are not available
 * * YELLOW when one or more replica shards are not available
 * * GREEN otherwise
 * <p>
 * Each shard needs to be available and replicated in order to guarantee high availability and prevent data loses.
 * Shards allocated on nodes scheduled for restart (using nodes shutdown API) will not degrade this indicator health.
 */
public class ShardsAvailabilityHealthIndicatorService implements HealthIndicatorService {