### 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
Set.of(),
                    allocation.nodeId
                )
            );
        }
        throw new AssertionError("Unexpected state [" + allocation.state + "]");
    }
    private static RecoverySource getSource(boolean primary, ShardState state) {
        if (primary) {
            return state == CREATING
                ? RecoverySource.EmptyStoreRecoverySource.INSTANCE
                : RecoverySource.ExistingStoreRecoverySource.INSTANCE;
        } else {
            return RecoverySource.PeerRecoverySource.INSTANCE;
        }
    }
    public enum ShardState {
        UNAVAILABLE,
        CREATING,
        AVAILABLE,
        RESTARTING,
        INITIALIZING,
    }
    private record ShardAllocation(String nodeId, ShardState state, Long unassignedTimeNanos, @Nullable UnassignedInfo unassignedInfo) {
        ShardAllocation(String nodeId, ShardState state) {
            this(nodeId, state, null, null);
        }
        ShardAllocation(String nodeId, ShardState state, Long unassignedTimeNanos) {
            this(nodeId, state, unassignedTimeNanos, null);
        }