### Elasticsearch Version

8.4, 8.5, 8.6

### Installed Plugins

_No response_

### Java Version

_bundled_

### OS Version

Darwin

### Problem Description

The shards availability indicator should always be reporting diagnosis when its status is RED/YELLOW.
However, when an index is on a data node that runs out of disk space it will report RED but no diagnosis.

### Steps to Reproduce

Have multi-node cluster where a data (non-master) node that hosts an index runs out of disk space (the index cannot relocate somewhere else).
Call the Health API and the output will be something along these lines:
```
    "shards_availability": {
      "status": "red",
      "symptom": "This cluster has all shards available.",
      "details": {
        "initializing_primaries": 1,
        "started_replicas": 0,
        "initializing_replicas": 0,
        "unassigned_primaries": 0,
        "started_primaries": 1,
        "creating_primaries": 0,
        "unassigned_replicas": 0,
        "restarting_primaries": 0,
        "restarting_replicas": 0
      },
      "impacts": [
        {
          "id": "elasticsearch:health:shards_availability:impact:primary_unassigned",
          "severity": 1,
          "description": "Cannot add data to 1 index [test_index]. Searches might return incomplete results.",
          "impact_areas": [
            "ingest",
            "search"
          ]
        }
      ] 
    }
``` 

### Logs (if relevant)

_No response_
server/src/main/java/org/elasticsearch/cluster/routing/allocation/ShardsAvailabilityHealthIndicatorService.java
boolean isRestarting = isUnassignedDueToTimelyRestart(routing, shutdowns);
            available &= routing.active() || isRestarting || isNew;
            if ((routing.active() || isRestarting || isNew) == false) {
                indicesWithUnavailableShards.add(routing.getIndexName());
            }
            switch (routing.state()) {
                case UNASSIGNED -> {
                    if (isNew) {
                        unassigned_new++;
                    } else if (isRestarting) {
                        unassigned_restarting++;
                    } else {
                        unassigned++;
                        if (verbose) {
                            diagnoseUnassignedShardRouting(routing, state).forEach(
                                definition -> addDefinition(definition, routing.getIndexName())
                            );
                        }
                    }
                }
                case INITIALIZING -> initializing++;
                case STARTED -> started++;
                case RELOCATING -> relocating++;
            }
        }
        private void addDefinition(Diagnosis.Definition diagnosisDefinition, String indexName) {
            diagnosisDefinitions.computeIfAbsent(diagnosisDefinition, (k) -> new HashSet<>()).add(indexName);
        }
    }
    private static boolean isUnassignedDueToTimelyRestart(ShardRouting routing, NodesShutdownMetadata shutdowns) {