### 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 static org.elasticsearch.cluster.routing.allocation.ShardsAvailabilityHealthIndicatorService.ACTION_MIGRATE_TIERS_AWAY_FROM_REQUIRE_DATA;
import static org.elasticsearch.cluster.routing.allocation.ShardsAvailabilityHealthIndicatorService.ACTION_MIGRATE_TIERS_AWAY_FROM_REQUIRE_DATA_LOOKUP;
import static org.elasticsearch.cluster.routing.allocation.ShardsAvailabilityHealthIndicatorService.ACTION_RESTORE_FROM_SNAPSHOT;
import static org.elasticsearch.cluster.routing.allocation.ShardsAvailabilityHealthIndicatorService.DIAGNOSIS_WAIT_FOR_INITIALIZATION;
import static org.elasticsearch.cluster.routing.allocation.ShardsAvailabilityHealthIndicatorService.DIAGNOSIS_WAIT_FOR_OR_FIX_DELAYED_SHARDS;
import static org.elasticsearch.cluster.routing.allocation.ShardsAvailabilityHealthIndicatorService.NAME;
import static org.elasticsearch.cluster.routing.allocation.ShardsAvailabilityHealthIndicatorServiceTests.ShardState.AVAILABLE;
import static org.elasticsearch.cluster.routing.allocation.ShardsAvailabilityHealthIndicatorServiceTests.ShardState.CREATING;
import static org.elasticsearch.cluster.routing.allocation.ShardsAvailabilityHealthIndicatorServiceTests.ShardState.INITIALIZING;
import static org.elasticsearch.cluster.routing.allocation.ShardsAvailabilityHealthIndicatorServiceTests.ShardState.RESTARTING;
import static org.elasticsearch.cluster.routing.allocation.ShardsAvailabilityHealthIndicatorServiceTests.ShardState.UNAVAILABLE;
import static org.elasticsearch.cluster.routing.allocation.decider.ShardsLimitAllocationDecider.CLUSTER_TOTAL_SHARDS_PER_NODE_SETTING;
import static org.elasticsearch.common.util.CollectionUtils.concatLists;
import static org.elasticsearch.core.TimeValue.timeValueSeconds;
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.hamcrest.Matchers.contains;
import static org.hamcrest.Matchers.containsInAnyOrder;
import static org.hamcrest.Matchers.emptyCollectionOf;
import static org.hamcrest.Matchers.equalTo;
import static org.hamcrest.Matchers.hasItems;
import static org.hamcrest.Matchers.hasSize;
import static org.hamcrest.Matchers.is;
import static org.mockito.ArgumentMatchers.any;
import static org.mockito.Mockito.mock;
import static org.mockito.Mockito.when;
public class ShardsAvailabilityHealthIndicatorServiceTests extends ESTestCase {