Backend: telegram_diagnose returns JSON with 8 checks (token, admin_ids, sing-box, port, DNS with FakeIP support, direct API, proxy API, send test message). Registered in CLI dispatcher. Frontend: Test Connection button in Telegram settings calls telegram_diagnose and renders results with check/cross icons. DNS check accepts sing-box FakeIP range (198.18.x.x/198.19.x.x).