P2.1: Add GatewayConnector BackgroundService with WebSocket client

- GatewayConnector: BackgroundService maintaining persistent WebSocket connection
  to OpenClaw Gateway with Bearer token auth from backend env only
- IGatewayConnector: Interface exposing connection state, version info, health
- Exponential backoff reconnect: 1s initial, max 5min, with jitter
- Version pinning: RequiredVersion from config; fail-fast or warn on mismatch
- Pre-flight HTTP version check before WebSocket connect
- GatewayHealthController: GET /api/health/gateway with connection status
- GatewayConnectorOptions: Configurable via GatewayConnector config section
- Token never logged; read from Integrations:OpenClaw:Password/Token only
- 16 tests: options defaults, config binding, health endpoint responses,
  connection states, DI registration, routing attributes

backend/Controllers/GatewayHealthController.cs

@@ -0,0 +1,33 @@
+using Microsoft.AspNetCore.Authorization;
+using Microsoft.AspNetCore.Mvc;
+using Nexus.Api.Services;
+
+namespace Nexus.Api.Controllers;
+
+/// <summary>
+/// Health-check endpoint for the Gateway WebSocket connection.
+/// </summary>
+[ApiController]
+[AllowAnonymous]
+public class GatewayHealthController(IGatewayConnector connector) : ControllerBase
+{
+    /// <summary>
+    /// Returns the current Gateway WebSocket connection health.
+    /// </summary>
+    [HttpGet("/api/health/gateway")]
+    public IResult GetGatewayHealth()
+    {
+        return Results.Ok(new
+        {
+            status = connector.ConnectionState.ToString().ToLowerInvariant(),
+            connected = connector.ConnectionState == GatewayConnectionState.Connected,
+            gatewayVersion = connector.GatewayVersion ?? "unknown",
+            requiredVersion = connector.RequiredVersion,
+            versionPinned = connector.RequiredVersion is not null,
+            lastConnectedAt = connector.LastConnectedAt?.ToString("o"),
+            reconnectAttempts = connector.ReconnectAttempts,
+            message = connector.StatusMessage,
+            timestamp = DateTimeOffset.UtcNow.ToString("o")
+        });
+    }
+}