### 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
List.of(),
            List.of()
        );
        
        Metadata.Builder mdBuilder = Metadata.builder(clusterState.metadata())
            .put(newInstance(featureDataStreamName, List.of(backingIndex.getIndex())));
        ClusterState state = ClusterState.builder(clusterState).metadata(mdBuilder).build();
        var service = createAllocationHealthIndicatorService(
            Settings.EMPTY,
            state,
            Map.of(),
            getSystemIndices(featureDataStreamName, ".test-ds-*", ".feature-*")
        );
        HealthIndicatorResult result = service.calculate(true, HealthInfo.EMPTY_HEALTH_INFO);
        assertThat(result.status(), is(HealthStatus.RED));
        assertThat(result.diagnosisList().size(), is(1));
        Diagnosis diagnosis = result.diagnosisList().get(0);
        List<Diagnosis.Resource> affectedResources = diagnosis.affectedResources();
        assertThat("expecting we report a resource of type INDEX and one of type FEATURE_STATE", affectedResources.size(), is(2));
        for (Diagnosis.Resource resource : affectedResources) {
            if (resource.getType() == INDEX) {
                assertThat(resource.getValues(), hasItems("regular-index"));
            } else {
                assertThat(resource.getType(), is(FEATURE_STATE));
                assertThat(resource.getValues(), hasItems("feature-with-system-data-stream", "feature-with-system-index"));
            }
        }
    }
    public void testGetRestoreFromSnapshotAffectedResources() {
        String featureDataStreamName = ".test-ds-feature";