### 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
tier -> new Diagnosis.Definition(
                    NAME,
                    "enable_data_tiers:tier:" + tier,
                    "Elasticsearch isn't allowed to allocate some shards from these indices because the indices expect to be allocated to "
                        + "data tier nodes, but there were not any nodes with the expected tiers found in the cluster.",
                    "Add nodes with the [" + tier + "] role to the cluster.",
                    ENABLE_TIER_ACTION_GUIDE
                )
            )
        );
    public static final String INCREASE_SHARD_LIMIT_ACTION_GUIDE = "https://ela.st/index-total-shards";
    public static final Diagnosis.Definition ACTION_INCREASE_SHARD_LIMIT_INDEX_SETTING = new Diagnosis.Definition(
        NAME,
        "increase_shard_limit_index_setting",
        "Elasticsearch isn't allowed to allocate some shards from these indices to any data nodes because each node has reached the index "
            + "shard limit. ",
        "Increase the values for the ["
            + INDEX_TOTAL_SHARDS_PER_NODE_SETTING.getKey()
            + "] index setting on each index or add more nodes to the target tiers.",
        INCREASE_SHARD_LIMIT_ACTION_GUIDE
    );
    public static final Map<String, Diagnosis.Definition> ACTION_INCREASE_SHARD_LIMIT_INDEX_SETTING_LOOKUP = DataTier.ALL_DATA_TIERS
        .stream()
        .collect(
            Collectors.toUnmodifiableMap(
                tier -> tier,
                tier -> new Diagnosis.Definition(
                    NAME,
                    "increase_shard_limit_index_setting:tier:" + tier,
                    "Elasticsearch isn't allowed to allocate some shards from these indices because each node in the ["