feat(client): add write timeout recovery with per-kind policies

Add WriteTimeoutPolicy enum, FlushResult record struct, and
GetWriteTimeoutPolicy static method as nested types in NatsClient.
Models Go's client.go per-kind timeout handling: CLIENT kind closes
on timeout, ROUTER/GATEWAY/LEAF use TCP-level flush recovery.

src/NATS.Server/NatsClient.cs

@@ -967,6 +967,47 @@ public sealed class NatsClient : INatsClient, IDisposable
         _socket.Dispose();
     }
 
+    /// <summary>
+    /// Policy for handling write timeouts based on client kind.
+    /// Go reference: server/client.go — CLIENT connections close on timeout,
+    /// ROUTER/GATEWAY/LEAF connections attempt TCP-level flush recovery.
+    /// </summary>
+    public enum WriteTimeoutPolicy
+    {
+        /// <summary>Close the connection on write timeout (used for CLIENT kind).</summary>
+        Close,
+
+        /// <summary>Attempt TCP-level flush and continue (used for ROUTER, GATEWAY, LEAF).</summary>
+        TcpFlush,
+    }
+
+    /// <summary>
+    /// Returns the write timeout policy for the given client kind.
+    /// Go reference: server/client.go — routes/gateways/leafnodes get TcpFlush,
+    /// regular clients get Close.
+    /// </summary>
+    public static WriteTimeoutPolicy GetWriteTimeoutPolicy(ClientKind kind) => kind switch
+    {
+        ClientKind.Client => WriteTimeoutPolicy.Close,
+        ClientKind.Router => WriteTimeoutPolicy.TcpFlush,
+        ClientKind.Gateway => WriteTimeoutPolicy.TcpFlush,
+        ClientKind.Leaf => WriteTimeoutPolicy.TcpFlush,
+        _ => WriteTimeoutPolicy.Close,
+    };
+
+    /// <summary>
+    /// Result of a flush operation, tracking partial write progress.
+    /// Go reference: server/client.go — partial write handling for routes and gateways.
+    /// </summary>
+    public readonly record struct FlushResult(long BytesAttempted, long BytesWritten)
+    {
+        /// <summary>Whether the flush was only partially completed.</summary>
+        public bool IsPartial => BytesWritten < BytesAttempted;
+
+        /// <summary>Number of bytes remaining to be written.</summary>
+        public long BytesRemaining => BytesAttempted - BytesWritten;
+    }
+
     /// <summary>
     /// Blocks producers when the client's outbound buffer is near capacity.
     /// Go reference: server/client.go (stc channel, stalledRoute handling).