### 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
);
        assertThat(actions, hasSize(1));
        assertThat(actions, contains(ACTION_ENABLE_CLUSTER_ROUTING_ALLOCATION));
    }
    public void testDiagnoseEnableRoutingAllocation() {
        
        IndexMetadata indexMetadata = IndexMetadata.builder("red-index")
            .settings(
                Settings.builder()
                    .put(IndexMetadata.SETTING_VERSION_CREATED, IndexVersion.current())
                    .put(EnableAllocationDecider.INDEX_ROUTING_ALLOCATION_ENABLE_SETTING.getKey(), "none")
                    .build()
            )
            .numberOfShards(1)
            .numberOfReplicas(0)
            .build();
        
        var service = createShardsAvailabilityIndicatorService(
            Settings.builder().put(EnableAllocationDecider.CLUSTER_ROUTING_ALLOCATION_ENABLE_SETTING.getKey(), "none").build(),
            ClusterState.EMPTY_STATE,
            Map.of()
        );
        
        List<Diagnosis.Definition> actions = service.checkIsAllocationDisabled(
            indexMetadata,
            List.of(
                new NodeAllocationResult(
                    
                    DiscoveryNodeUtils.create(randomNodeId()),
                    new Decision.Multi().add(Decision.single(Decision.Type.NO, EnableAllocationDecider.NAME, null)),