### 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/test/java/org/elasticsearch/cluster/routing/allocation/ShardsAvailabilityHealthIndicatorServiceTests.java
import org.elasticsearch.cluster.routing.ShardRouting;
import org.elasticsearch.cluster.routing.UnassignedInfo;
import org.elasticsearch.cluster.routing.allocation.ShardsAvailabilityHealthIndicatorService.ShardAllocationStatus;
import org.elasticsearch.cluster.routing.allocation.decider.AwarenessAllocationDecider;
import org.elasticsearch.cluster.routing.allocation.decider.Decision;
import org.elasticsearch.cluster.routing.allocation.decider.EnableAllocationDecider;
import org.elasticsearch.cluster.routing.allocation.decider.FilterAllocationDecider;
import org.elasticsearch.cluster.routing.allocation.decider.SameShardAllocationDecider;
import org.elasticsearch.cluster.routing.allocation.decider.ShardsLimitAllocationDecider;
import org.elasticsearch.cluster.service.ClusterService;
import org.elasticsearch.common.settings.ClusterSettings;
import org.elasticsearch.common.settings.Settings;
import org.elasticsearch.core.Nullable;
import org.elasticsearch.health.Diagnosis;
import org.elasticsearch.health.HealthIndicatorDetails;
import org.elasticsearch.health.HealthIndicatorImpact;
import org.elasticsearch.health.HealthIndicatorResult;
import org.elasticsearch.health.HealthStatus;
import org.elasticsearch.health.ImpactArea;
import org.elasticsearch.health.SimpleHealthIndicatorDetails;
import org.elasticsearch.health.node.HealthInfo;
import org.elasticsearch.index.Index;
import org.elasticsearch.index.IndexVersion;
import org.elasticsearch.index.shard.ShardId;
import org.elasticsearch.indices.ExecutorNames;
import org.elasticsearch.indices.SystemDataStreamDescriptor;
import org.elasticsearch.indices.SystemIndexDescriptorUtils;
import org.elasticsearch.indices.SystemIndices;
import org.elasticsearch.test.ESTestCase;
import org.elasticsearch.threadpool.ThreadPool;