### 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
AllocateUnassignedDecision allocateDecision = shardAllocationDecision.getAllocateDecision();
        if (LOGGER.isTraceEnabled()) {
            if (allocateDecision.isDecisionTaken()) {
                LOGGER.trace("[{}]: Allocation decision [{}]", shardRouting.shardId(), allocateDecision.getAllocationDecision());
            } else {
                LOGGER.trace("[{}]: Decision taken [false]", shardRouting.shardId());
            }
        }
        if (allocateDecision.isDecisionTaken() && AllocationDecision.NO == allocateDecision.getAllocationDecision()) {
            if (LOGGER.isTraceEnabled()) {
                LOGGER.trace(
                    "[{}]: Working with decisions: [{}]",
                    shardRouting.shardId(),
                    allocateDecision.getNodeDecisions()
                        .stream()
                        .map(
                            n -> n.getCanAllocateDecision()
                                .getDecisions()
                                .stream()
                                .map(d -> d.label() + ": " + d.type())
                                .collect(Collectors.toList())
                        )
                        .collect(Collectors.toList())
                );
            }
            List<NodeAllocationResult> nodeAllocationResults = allocateDecision.getNodeDecisions();
            return diagnoseAllocationResults(shardRouting, state, nodeAllocationResults);
        } else {
            return List.of();
        }