### 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
.collect(Collectors.toSet());
                
                Set<String> dataTierRolesAvailable = dataTierNodes.stream()
                    .map(DiscoveryNode::getRoles)
                    .flatMap(Set::stream)
                    .map(DiscoveryNodeRole::roleName)
                    .collect(Collectors.toSet());
                
                String preferredTier = indexMetadata.getTierPreference()
                    .stream()
                    .filter(dataTierRolesAvailable::contains)
                    .findFirst()
                    .orElse(null);
                
                diagnosisDefs.addAll(
                    checkDataTierAtShardLimit(indexMetadata, clusterState, dataTierAllocationResults, dataTierNodes, preferredTier)
                );
                diagnosisDefs.addAll(checkDataTierShouldMigrate(indexMetadata, dataTierAllocationResults, preferredTier, dataTierNodes));
                checkNotEnoughNodesInDataTier(dataTierAllocationResults, preferredTier).ifPresent(diagnosisDefs::add);
            }
        }
        return diagnosisDefs;
    }
    private List<Diagnosis.Definition> checkDataTierAtShardLimit(
        IndexMetadata indexMetadata,
        ClusterState clusterState,
        List<NodeAllocationResult> dataTierAllocationResults,
        Set<DiscoveryNode> dataTierNodes,
        @Nullable String preferredTier
    ) {