### 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
var info = routing.unassignedInfo();
        if (info == null || info.getReason() != UnassignedInfo.Reason.NODE_RESTARTING) {
            return false;
        }
        var shutdown = shutdowns.getAllNodeMetadataMap().get(info.getLastAllocatedNodeId());
        if (shutdown == null || shutdown.getType() != SingleNodeShutdownMetadata.Type.RESTART) {
            return false;
        }
        var now = System.nanoTime();
        var restartingAllocationDelayExpiration = info.getUnassignedTimeInNanos() + shutdown.getAllocationDelay().nanos();
        return now <= restartingAllocationDelayExpiration;
    }
    private static boolean isUnassignedDueToNewInitialization(ShardRouting routing) {
        return routing.primary() && routing.active() == false && getInactivePrimaryHealth(routing) == ClusterHealthStatus.YELLOW;
    }
    /**
     * Generate a list of diagnoses that'll contain the instructions for a user to take to allow this shard to be assigned.
     * @param shardRouting An unassigned shard routing
     * @param state State of the cluster
     * @return A list of diagnoses for the provided unassigned shard
     */
    List<Diagnosis.Definition> diagnoseUnassignedShardRouting(ShardRouting shardRouting, ClusterState state) {
        List<Diagnosis.Definition> diagnosisDefs = new ArrayList<>();
        LOGGER.trace("Diagnosing unassigned shard [{}] due to reason [{}]", shardRouting.shardId(), shardRouting.unassignedInfo());
        switch (shardRouting.unassignedInfo().getLastAllocationStatus()) {
            case NO_VALID_SHARD_COPY:
                diagnosisDefs.add(ACTION_RESTORE_FROM_SNAPSHOT);
                break;
            case NO_ATTEMPT:
                if (shardRouting.unassignedInfo().isDelayed()) {