feat: add MBE health check proxy endpoint

- Added /api/v1/mbe/health proxy in Studio proxy (port 8888)
- Frontend now uses proxy endpoint instead of direct mbeUrl
- Works for both localhost and external access (once proxy is deployed)
- MBE health response: {status: 'healthy', model: 'e4b', layers: 42}

src-tauri/src/proxy.rs

@@ -263,6 +263,24 @@ async fn fallback_handler(State(state): State<ProxyState>, req: axum::extract::R
         return handle_local_api(req).await;
     }
 
+    // Handle MBE health check proxy
+    if path == "/api/v1/mbe/health" {
+        let client = reqwest::Client::new();
+        match client.get("http://localhost:8080/health").send().await {
+            Ok(resp) => {
+                let status = resp.status().as_u16();
+                let body = resp.bytes().await.unwrap_or_default();
+                let status_code = axum::http::StatusCode::from_u16(status).unwrap_or(axum::http::StatusCode::INTERNAL_SERVER_ERROR);
+                let mut builder = axum::http::Response::builder().status(status_code);
+                builder = builder.header("content-type", "application/json");
+                return builder.body(axum::body::Body::from(body)).unwrap().into_response();
+            }
+            Err(_) => {
+                return (StatusCode::SERVICE_UNAVAILABLE, "{\"status\":\"unreachable\"}").into_response();
+            }
+        }
+    }
+
     if path.starts_with("/api/v2/") {
         return proxy_to(state, req, MARKBASE_API, false).await;
     } else if path.starts_with("/api/") {