feat: e2e 테스트 실행 및 에러 수정

app/game-engine/src/paths.ts

@@ -0,0 +1,25 @@
+import fs from 'node:fs';
+import path from 'node:path';
+
+const WORKSPACE_MARKERS = ['pnpm-workspace.yaml'];
+
+const hasWorkspaceMarker = (dir: string): boolean =>
+    WORKSPACE_MARKERS.some((marker) => fs.existsSync(path.join(dir, marker)));
+
+export const resolveWorkspaceRoot = (
+    startDir: string = process.env.GATEWAY_WORKSPACE_ROOT ?? process.cwd(),
+    maxDepth = 6
+): string => {
+    let current = path.resolve(startDir);
+    for (let depth = 0; depth <= maxDepth; depth += 1) {
+        if (hasWorkspaceMarker(current)) {
+            return current;
+        }
+        const parent = path.dirname(current);
+        if (parent === current) {
+            break;
+        }
+        current = parent;
+    }
+    return path.resolve(startDir);
+};