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

Backend/LanderConfig.cs

@@ -0,0 +1,34 @@
+namespace Backend;
+
+public sealed class LanderConfig
+{
+    public string CliPath  { get; set; } = "publish/GameCli/GameCli";
+    public string ModelPath { get; set; } = "models/ppo_lander.onnx";
+}
+
+/// <summary>
+/// Walks up from <see cref="AppContext.BaseDirectory"/> to find the repo root
+/// (marker file: <c>GameCli.sln</c>) and resolves the configured paths against it.
+/// </summary>
+public static class PathResolver
+{
+    public static string RepoRoot()
+    {
+        var dir = AppContext.BaseDirectory;
+        while (dir is not null)
+        {
+            if (File.Exists(Path.Combine(dir, "GameCli.sln"))) return dir;
+            var parent = Directory.GetParent(dir);
+            if (parent is null) break;
+            dir = parent.FullName;
+        }
+        throw new InvalidOperationException(
+            "could not locate repo root (no GameCli.sln found in any ancestor)");
+    }
+
+    public static string Resolve(string relativeOrAbsolute)
+    {
+        if (Path.IsPathRooted(relativeOrAbsolute)) return relativeOrAbsolute;
+        return Path.GetFullPath(Path.Combine(RepoRoot(), relativeOrAbsolute));
+    }
+}