### 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
*/
    private static Predicate<NodeAllocationResult> hasDeciderResult(String deciderName, Decision.Type outcome) {
        return (nodeResult) -> {
            Decision decision = nodeResult.getCanAllocateDecision();
            return decision != null && decision.getDecisions().stream().anyMatch(d -> deciderName.equals(d.label()) && outcome == d.type());
        };
    }
    /**
     * Generates a list of diagnoses if a shard cannot be allocated anywhere because allocation is disabled for that shard
     * @param indexMetadata from the index shard being diagnosed
     * @param nodeAllocationResults allocation decision results for all nodes in the cluster.
     * @return A list of diagnoses for the provided unassigned shard
     */
    List<Diagnosis.Definition> checkIsAllocationDisabled(IndexMetadata indexMetadata, List<NodeAllocationResult> nodeAllocationResults) {
        List<Diagnosis.Definition> diagnosisDefs = new ArrayList<>();
        if (nodeAllocationResults.stream().allMatch(hasDeciderResult(EnableAllocationDecider.NAME, Decision.Type.NO))) {
            
            Settings indexSettings = indexMetadata.getSettings();
            EnableAllocationDecider.Allocation indexLevelAllocation = INDEX_ROUTING_ALLOCATION_ENABLE_SETTING.get(indexSettings);
            ClusterSettings clusterSettings = clusterService.getClusterSettings();
            EnableAllocationDecider.Allocation clusterLevelAllocation = clusterSettings.get(
                EnableAllocationDecider.CLUSTER_ROUTING_ALLOCATION_ENABLE_SETTING
            );
            if (EnableAllocationDecider.Allocation.ALL != indexLevelAllocation) {
                
                diagnosisDefs.add(ACTION_ENABLE_INDEX_ROUTING_ALLOCATION);
            }
            if (EnableAllocationDecider.Allocation.ALL != clusterLevelAllocation) {
                
                diagnosisDefs.add(ACTION_ENABLE_CLUSTER_ROUTING_ALLOCATION);