### 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
}
            }
            return diagnosisDefs;
        } else {
            return List.of();
        }
    }
    private static Optional<Diagnosis.Definition> checkNotEnoughNodesInDataTier(
        List<NodeAllocationResult> dataTierAllocationResults,
        @Nullable String preferredTier
    ) {
        
        if (dataTierAllocationResults.stream().allMatch(hasDeciderResult(SameShardAllocationDecider.NAME, Decision.Type.NO))) {
            
            
            if (preferredTier != null) {
                return Optional.ofNullable(ACTION_INCREASE_TIER_CAPACITY_LOOKUP.get(preferredTier));
            } else {
                return Optional.of(ACTION_INCREASE_NODE_CAPACITY);
            }
        } else {
            return Optional.empty();
        }
    }
    class ShardAllocationStatus {
        private final ShardAllocationCounts primaries = new ShardAllocationCounts();
        private final ShardAllocationCounts replicas = new ShardAllocationCounts();
        private final Metadata clusterMetadata;
        ShardAllocationStatus(Metadata clusterMetadata) {
            this.clusterMetadata = clusterMetadata;