Cherry-pick from codex/omniroute-fixes-20260324:
- Replace MCP singleton transport with per-session architecture for Streamable HTTP
- Fix Claude passthrough via OpenAI round-trip normalization
- Add detectFormatFromEndpoint() for endpoint-aware format detection
- Support raw code#state in OAuth modal for Claude Code remote auth
- Expose cloudConfigured/cloudUrl/machineId in settings API
- Switch docker-compose.prod.yml target to runner-cli
- Add 3 new tests for round-trip and detectFormat
PR: #562