### 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
/*
 * Copyright Elasticsearch B.V. and/or licensed to Elasticsearch B.V. under one
 * or more contributor license agreements. Licensed under the Elastic License
 * 2.0 and the Server Side Public License, v 1; you may not use this file except
 * in compliance with, at your election, the Elastic License 2.0 or the Server
 * Side Public License, v 1.
 */
package org.elasticsearch.cluster.routing.allocation;
import org.apache.logging.log4j.LogManager;
import org.apache.logging.log4j.Logger;
import org.elasticsearch.cluster.ClusterInfo;
import org.elasticsearch.cluster.ClusterState;
import org.elasticsearch.cluster.health.ClusterHealthStatus;
import org.elasticsearch.cluster.metadata.IndexMetadata;
import org.elasticsearch.cluster.metadata.Metadata;
import org.elasticsearch.cluster.metadata.NodesShutdownMetadata;
import org.elasticsearch.cluster.metadata.SingleNodeShutdownMetadata;
import org.elasticsearch.cluster.node.DiscoveryNode;
import org.elasticsearch.cluster.node.DiscoveryNodeFilters;
import org.elasticsearch.cluster.node.DiscoveryNodeRole;
import org.elasticsearch.cluster.routing.IndexRoutingTable;
import org.elasticsearch.cluster.routing.IndexShardRoutingTable;
import org.elasticsearch.cluster.routing.RoutingNode;
import org.elasticsearch.cluster.routing.ShardRouting;
import org.elasticsearch.cluster.routing.UnassignedInfo;
import org.elasticsearch.cluster.routing.allocation.decider.Decision;
import org.elasticsearch.cluster.routing.allocation.decider.EnableAllocationDecider;