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).

tests/NATS.Server.Tests/WriteTimeoutTests.cs

@@ -0,0 +1,61 @@
+namespace NATS.Server.Tests;
+
+// Go reference: server/client.go (write timeout handling, per-kind policies)
+
+public class WriteTimeoutTests
+{
+    [Fact]
+    public void WriteTimeoutPolicy_defaults_by_kind()
+    {
+        // Go reference: server/client.go — CLIENT closes, others use TCP flush
+        NatsClient.GetWriteTimeoutPolicy(ClientKind.Client).ShouldBe(NatsClient.WriteTimeoutPolicy.Close);
+        NatsClient.GetWriteTimeoutPolicy(ClientKind.Router).ShouldBe(NatsClient.WriteTimeoutPolicy.TcpFlush);
+        NatsClient.GetWriteTimeoutPolicy(ClientKind.Gateway).ShouldBe(NatsClient.WriteTimeoutPolicy.TcpFlush);
+        NatsClient.GetWriteTimeoutPolicy(ClientKind.Leaf).ShouldBe(NatsClient.WriteTimeoutPolicy.TcpFlush);
+    }
+
+    [Fact]
+    public void PartialFlushResult_tracks_bytes()
+    {
+        // Go reference: server/client.go — partial write tracking
+        var result = new NatsClient.FlushResult(BytesAttempted: 1024, BytesWritten: 512);
+        result.IsPartial.ShouldBeTrue();
+        result.BytesRemaining.ShouldBe(512L);
+    }
+
+    [Fact]
+    public void PartialFlushResult_complete_is_not_partial()
+    {
+        // Go reference: server/client.go — complete write
+        var result = new NatsClient.FlushResult(BytesAttempted: 1024, BytesWritten: 1024);
+        result.IsPartial.ShouldBeFalse();
+        result.BytesRemaining.ShouldBe(0L);
+    }
+
+    [Fact]
+    public void WriteTimeoutPolicy_system_kind_defaults_to_close()
+    {
+        // Go reference: server/client.go — system/internal kinds default to Close
+        NatsClient.GetWriteTimeoutPolicy(ClientKind.System).ShouldBe(NatsClient.WriteTimeoutPolicy.Close);
+        NatsClient.GetWriteTimeoutPolicy(ClientKind.JetStream).ShouldBe(NatsClient.WriteTimeoutPolicy.Close);
+        NatsClient.GetWriteTimeoutPolicy(ClientKind.Account).ShouldBe(NatsClient.WriteTimeoutPolicy.Close);
+    }
+
+    [Fact]
+    public void FlushResult_zero_bytes_is_partial_when_attempted_nonzero()
+    {
+        // Edge case: nothing written but something attempted
+        var result = new NatsClient.FlushResult(BytesAttempted: 100, BytesWritten: 0);
+        result.IsPartial.ShouldBeTrue();
+        result.BytesRemaining.ShouldBe(100L);
+    }
+
+    [Fact]
+    public void FlushResult_zero_zero_is_not_partial()
+    {
+        // Edge case: nothing attempted, nothing written
+        var result = new NatsClient.FlushResult(BytesAttempted: 0, BytesWritten: 0);
+        result.IsPartial.ShouldBeFalse();
+        result.BytesRemaining.ShouldBe(0L);
+    }
+}