### 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
if (dataTierAllocationResults.stream().allMatch(hasDeciderResult(FilterAllocationDecider.NAME, Decision.Type.NO))) {
            List<Diagnosis.Definition> diagnosisDefs = new ArrayList<>();
            Map<String, List<String>> requireAttributes = INDEX_ROUTING_REQUIRE_GROUP_SETTING.getAsMap(indexMetadata.getSettings());
            List<String> requireDataAttributes = requireAttributes.get("data");
            DiscoveryNodeFilters requireFilter = requireDataAttributes == null
                ? null
                : DiscoveryNodeFilters.buildFromKeyValues(DiscoveryNodeFilters.OpType.AND, Map.of("data", requireDataAttributes));
            Map<String, List<String>> includeAttributes = INDEX_ROUTING_INCLUDE_GROUP_SETTING.getAsMap(indexMetadata.getSettings());
            List<String> includeDataAttributes = includeAttributes.get("data");
            DiscoveryNodeFilters includeFilter = includeDataAttributes == null
                ? null
                : DiscoveryNodeFilters.buildFromKeyValues(DiscoveryNodeFilters.OpType.OR, Map.of("data", includeDataAttributes));
            if (requireFilter != null || includeFilter != null) {
                
                if (requireFilter != null && dataTierNodes.stream().noneMatch(requireFilter::match)) {
                    
                    diagnosisDefs.add(
                        Optional.ofNullable(preferredTier)
                            .map(ACTION_MIGRATE_TIERS_AWAY_FROM_REQUIRE_DATA_LOOKUP::get)
                            .orElse(ACTION_MIGRATE_TIERS_AWAY_FROM_REQUIRE_DATA)
                    );
                }
                if (includeFilter != null && dataTierNodes.stream().noneMatch(includeFilter::match)) {
                    
                    diagnosisDefs.add(
                        Optional.ofNullable(preferredTier)
                            .map(ACTION_MIGRATE_TIERS_AWAY_FROM_INCLUDE_DATA_LOOKUP::get)
                            .orElse(ACTION_MIGRATE_TIERS_AWAY_FROM_INCLUDE_DATA)
                    );