feat(backend): wire ASP.NET startup with WebSocket endpoint and DI

Backend/Program.cs

@@ -1,5 +1,52 @@
-// Placeholder. Rewritten in Task 6.
+using System.Net.WebSockets;
+using Backend;
+
 var builder = WebApplication.CreateBuilder(args);
+
+// -------- Config --------
+builder.Services.Configure<LanderConfig>(builder.Configuration.GetSection("Lander"));
+
+// -------- Singletons --------
+builder.Services.AddSingleton<PolicyRunner>(sp =>
+{
+    var cfg = sp.GetRequiredService<Microsoft.Extensions.Options.IOptions<LanderConfig>>().Value;
+    var absolute = PathResolver.Resolve(cfg.ModelPath);
+    return new PolicyRunner(absolute);
+});
+
+builder.Services.AddLogging();
+
 var app = builder.Build();
-app.MapGet("/", () => "GameCli Backend placeholder");
+app.UseWebSockets();
+
+// -------- Health --------
+app.MapGet("/", () => "GameCli Backend");
+
+// -------- WebSocket endpoint --------
+app.Map("/ws/game", async (HttpContext ctx,
+                          PolicyRunner policy,
+                          Microsoft.Extensions.Options.IOptions<LanderConfig> cfg,
+                          ILoggerFactory loggerFactory) =>
+{
+    if (!ctx.WebSockets.IsWebSocketRequest)
+    {
+        ctx.Response.StatusCode = 400;
+        return;
+    }
+    using var socket = await ctx.WebSockets.AcceptWebSocketAsync();
+    var cliPath = PathResolver.Resolve(cfg.Value.CliPath);
+    var proc = new GameProcess(cliPath);
+    var logger = loggerFactory.CreateLogger<GameSession>();
+    await using var session = new GameSession(socket, proc, policy, logger);
+    try
+    {
+        await session.RunAsync(ctx.RequestAborted);
+    }
+    catch (WebSocketException) { /* client disconnected */ }
+    catch (OperationCanceledException) { /* shutdown */ }
+});
+
 app.Run();
+
+// -------- Public program class so Backend.Tests can use WebApplicationFactory --------
+public partial class Program { }