### 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
}
    /**
     * Generates a list of diagnoses for an unassigned shard by inspecting a list of NodeAllocationResults for
     * well known problems.
     * @param shardRouting The unassigned shard.
     * @param state Current cluster state.
     * @param nodeAllocationResults A list of results for each node in the cluster from the allocation explain api
     * @return A list of diagnoses for the provided unassigned shard
     */
    List<Diagnosis.Definition> diagnoseAllocationResults(
        ShardRouting shardRouting,
        ClusterState state,
        List<NodeAllocationResult> nodeAllocationResults
    ) {
        IndexMetadata index = state.metadata().index(shardRouting.index());
        List<Diagnosis.Definition> diagnosisDefs = new ArrayList<>();
        if (index != null) {
            diagnosisDefs.addAll(checkIsAllocationDisabled(index, nodeAllocationResults));
            diagnosisDefs.addAll(checkDataTierRelatedIssues(index, nodeAllocationResults, state));
        }
        if (diagnosisDefs.isEmpty()) {
            diagnosisDefs.add(ACTION_CHECK_ALLOCATION_EXPLAIN_API);
        }
        return diagnosisDefs;
    }
    /**
     * Convenience method for filtering node allocation results by decider outcomes.
     * @param deciderName The decider that is being checked
     * @param outcome The outcome expected
     * @return A predicate that returns true if the decision exists and matches the expected outcome, false otherwise.