### 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
maxAffectedResourcesCount
                                );
                            }
                        } else {
                            affectedResources.add(
                                new Diagnosis.Resource(
                                    INDEX,
                                    e.getValue()
                                        .stream()
                                        .sorted(indicesComparatorByPriorityAndName(clusterMetadata))
                                        .limit(Math.min(e.getValue().size(), maxAffectedResourcesCount))
                                        .collect(Collectors.toList())
                                )
                            );
                        }
                        return new Diagnosis(e.getKey(), affectedResources);
                    }).collect(Collectors.toList());
                }
            } else {
                return List.of();
            }
        }
        /**
         * The restore from snapshot operation requires the user to specify indices and feature states.
         * The indices that are part of the feature states must not be specified. This method loops through all the
         * identified unassigned indices and returns the affected {@link Diagnosis.Resource}s of type `INDEX`
         * and if applicable `FEATURE_STATE`
         */
        static List<Diagnosis.Resource> getRestoreFromSnapshotAffectedResources(
            Metadata metadata,