### 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
List.of(
                IndexRoutingTable.builder(index)
                    
                    .addShard(createShardRouting(new ShardId(index, 0), true, new ShardAllocation(hotNode.getId(), AVAILABLE)))
                    
                    .addShard(
                        createShardRouting(new ShardId(index, 1), true, new ShardAllocation(randomNodeId(), UNAVAILABLE, decidersNo()))
                    )
                    .build()
            ),
            List.of(),
            List.of(hotNode)
        );
        var service = createShardsAvailabilityIndicatorService();
        
        List<Diagnosis.Definition> actions = service.checkDataTierRelatedIssues(
            indexMetadata,
            List.of(
                new NodeAllocationResult(
                    hotNode,
                    
                    new Decision.Multi().add(Decision.single(Decision.Type.YES, "data_tier", null))
                        .add(Decision.single(Decision.Type.NO, ShardsLimitAllocationDecider.NAME, null)),
                    1
                )
            ),
            clusterState
        );
        assertThat(actions, hasSize(1));
        assertThat(actions, contains(ACTION_INCREASE_SHARD_LIMIT_INDEX_SETTING_LOOKUP.get(DataTier.DATA_HOT)));