## 1. Backend - Proxy Endpoint

- [x] 1.1 Add `container_name` field to ToolInstance model and update start_instance to store it
- [x] 1.2 Create proxy endpoint `/instances/{id}/proxy/{path:path}` in tool_instances.py
- [x] 1.3 Implement HTTP forwarding using httpx with streaming support
- [x] 1.4 Add ownership check before proxying
- [x] 1.5 Add WebSocket upgrade support for the proxy endpoint
- [x] 1.6 Handle response header forwarding (Content-Type, cookies, etc.)

## 2. Backend - Instance URL Update

- [x] 2.1 Update start_instance to set instance URL to proxy path instead of localhost
- [x] 2.2 Ensure container_name is captured during start

## 3. Frontend - Update Instance Links

- [x] 3.1 Update InstanceList "Open" button to use proxy URL
- [x] 3.2 Update SessionsPage "Open" button to use proxy URL
- [x] 3.3 Ensure URLs open in new tab

## 4. Testing & Quality

- [x] 4.1 Test proxy with code-server instance
- [x] 4.2 Verify WebSocket features work (terminal inside code-server)
- [x] 4.3 Run quality gates (ruff, mypy, typecheck, lint, build)
- [x] 4.4 Deploy and test end-to-end