### 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(
                        new SystemDataStreamDescriptor(
                            featureDataStreamName,
                            "description",
                            SystemDataStreamDescriptor.Type.EXTERNAL,
                            new ComposableIndexTemplate(
                                List.of(systemDataStreamPattern),
                                null,
                                null,
                                null,
                                null,
                                null,
                                new ComposableIndexTemplate.DataStreamTemplate()
                            ),
                            Map.of(),
                            List.of("test"),
                            new ExecutorNames(
                                ThreadPool.Names.SYSTEM_CRITICAL_READ,
                                ThreadPool.Names.SYSTEM_READ,
                                ThreadPool.Names.SYSTEM_WRITE
                            )
                        )
                    )
                )
            )
        );
    }
    
    
    public void testMappedFieldsForTelemetry() {