feat: add stale connection stats tracking and varz exposure

src/NATS.Server/Monitoring/Varz.cs

@@ -157,6 +157,12 @@ public sealed class Varz
     [JsonPropertyName("slow_consumer_stats")]
     public SlowConsumersStats SlowConsumerStats { get; set; } = new();
 
+    [JsonPropertyName("stale_connections")]
+    public long StaleConnections { get; set; }
+
+    [JsonPropertyName("stale_connection_stats")]
+    public StaleConnectionStats StaleConnectionStatsDetail { get; set; } = new();
+
     [JsonPropertyName("subscriptions")]
     public uint Subscriptions { get; set; }
 
@@ -219,6 +225,25 @@ public sealed class SlowConsumersStats
     public ulong Leafs { get; set; }
 }
 
+/// <summary>
+/// Statistics about stale connections by connection type.
+/// Corresponds to Go server/monitor.go StaleConnectionStats struct.
+/// </summary>
+public sealed class StaleConnectionStats
+{
+    [JsonPropertyName("clients")]
+    public ulong Clients { get; set; }
+
+    [JsonPropertyName("routes")]
+    public ulong Routes { get; set; }
+
+    [JsonPropertyName("gateways")]
+    public ulong Gateways { get; set; }
+
+    [JsonPropertyName("leafs")]
+    public ulong Leafs { get; set; }
+}
+
 /// <summary>
 /// Cluster configuration monitoring information.
 /// Corresponds to Go server/monitor.go ClusterOptsVarz struct.

src/NATS.Server/Monitoring/VarzHandler.cs

@@ -91,6 +91,14 @@ public sealed class VarzHandler : IDisposable
                     Gateways = (ulong)Interlocked.Read(ref stats.SlowConsumerGateways),
                     Leafs = (ulong)Interlocked.Read(ref stats.SlowConsumerLeafs),
                 },
+                StaleConnections = Interlocked.Read(ref stats.StaleConnections),
+                StaleConnectionStatsDetail = new StaleConnectionStats
+                {
+                    Clients = (ulong)Interlocked.Read(ref stats.StaleConnectionClients),
+                    Routes = (ulong)Interlocked.Read(ref stats.StaleConnectionRoutes),
+                    Gateways = (ulong)Interlocked.Read(ref stats.StaleConnectionGateways),
+                    Leafs = (ulong)Interlocked.Read(ref stats.StaleConnectionLeafs),
+                },
                 Subscriptions = _server.SubList.Count,
                 ConfigLoadTime = _server.StartTime,
                 HttpReqStats = stats.HttpReqStats.ToDictionary(kv => kv.Key, kv => (ulong)kv.Value),