### 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_
x-pack/plugin/searchable-snapshots/src/main/java/org/elasticsearch/xpack/searchablesnapshots/SearchableSnapshots.java
private final RerouteService rerouteService;
        private final HashSet<String> knownUuids = new HashSet<>();
        RepositoryUuidWatcher(RerouteService rerouteService) {
            this.rerouteService = rerouteService;
        }
        @Override
        public void clusterChanged(ClusterChangedEvent event) {
            final RepositoriesMetadata repositoriesMetadata = event.state().metadata().custom(RepositoriesMetadata.TYPE);
            if (repositoriesMetadata == null) {
                knownUuids.clear();
                return;
            }
            final Set<String> newUuids = repositoriesMetadata.repositories()
                .stream()
                .map(RepositoryMetadata::uuid)
                .filter(s -> s.equals(RepositoryData.MISSING_UUID) == false)
                .collect(Collectors.toSet());
            if (knownUuids.addAll(newUuids)) {
                rerouteService.reroute("repository UUIDs changed", Priority.NORMAL, ActionListener.noop());
            }
            knownUuids.retainAll(newUuids);
            assert knownUuids.equals(newUuids) : knownUuids + " vs " + newUuids;
        }
    }
}