fix: restore dependency update compatibility

Fix VS Code webview type-check with TypeScript 5.9
Align ghostty-web to 0.4.0 across the workspace
Refresh ghostty-web patch for the updated package

package.json

@@ -108,7 +108,7 @@
     "clsx": "^2.1.1",
     "cmdk": "^1.1.1",
     "express": "^5.1.0",
-    "ghostty-web": "0.3.0",
+    "ghostty-web": "0.4.0",
     "http-proxy-middleware": "^3.0.5",
     "next-themes": "^0.4.6",
     "node-pty": "1.2.0-beta.12",