### 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
equalTo("elasticsearch:health:shards_availability:diagnosis:migrate_data_tiers_require_data:tier:" + tier)
            );
            assertThat(
                ACTION_MIGRATE_TIERS_AWAY_FROM_INCLUDE_DATA_LOOKUP.get(tier).getUniqueId(),
                equalTo("elasticsearch:health:shards_availability:diagnosis:migrate_data_tiers_include_data:tier:" + tier)
            );
            assertThat(
                ACTION_INCREASE_TIER_CAPACITY_LOOKUP.get(tier).getUniqueId(),
                equalTo("elasticsearch:health:shards_availability:diagnosis:increase_tier_capacity_for_allocations:tier:" + tier)
            );
        }
    }
    private HealthIndicatorResult createExpectedResult(
        HealthStatus status,
        String symptom,
        Map<String, Object> details,
        List<HealthIndicatorImpact> impacts,
        List<Diagnosis> diagnosisList
    ) {
        return new HealthIndicatorResult(
            NAME,
            status,
            symptom,
            new SimpleHealthIndicatorDetails(addDefaults(details)),
            impacts,
            diagnosisList
        );
    }
    private HealthIndicatorResult createExpectedTruncatedResult(HealthStatus status, String symptom, List<HealthIndicatorImpact> impacts) {
        return new HealthIndicatorResult(NAME, status, symptom, HealthIndicatorDetails.EMPTY, impacts, emptyList());