### 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/test/java/org/elasticsearch/cluster/routing/allocation/ShardsAvailabilityHealthIndicatorServiceTests.java
IndexMetadata backingIndex = createBackingIndex(featureDataStreamName, 1).build();
        List<IndexMetadata> indexMetadataList = List.of(
            IndexMetadata.builder(".feature-index")
                .settings(Settings.builder().put(IndexMetadata.SETTING_VERSION_CREATED, IndexVersion.current()).build())
                .numberOfShards(1)
                .numberOfReplicas(0)
                .build(),
            IndexMetadata.builder("regular-index")
                .settings(Settings.builder().put(IndexMetadata.SETTING_VERSION_CREATED, IndexVersion.current()).build())
                .numberOfShards(1)
                .numberOfReplicas(0)
                .build(),
            backingIndex
        );
        Metadata.Builder metadataBuilder = Metadata.builder();
        Map<String, IndexMetadata> indexMetadataMap = new HashMap<>();
        for (IndexMetadata indexMetadata : indexMetadataList) {
            indexMetadataMap.put(indexMetadata.getIndex().getName(), indexMetadata);
        }
        metadataBuilder.indices(indexMetadataMap);
        metadataBuilder.put(newInstance(featureDataStreamName, List.of(backingIndex.getIndex())));
        Metadata metadata = metadataBuilder.build();
        {
            List<Diagnosis.Resource> affectedResources = ShardAllocationStatus.getRestoreFromSnapshotAffectedResources(
                metadata,
                getSystemIndices(featureDataStreamName, ".test-ds-*", ".feature-*"),
                Set.of(backingIndex.getIndex().getName(), ".feature-index", "regular-index"),
                10
            );
            assertThat(affectedResources.size(), is(2));