fix(llm): avoid auth during ChatGPT lookup

LiteLLM treats provider-qualified metadata lookups as an auth path.
Use the underlying model slug so context sizing cannot block the scan
loop in a device-code poll.

tests/test_context_budget.py

@@ -21,6 +21,24 @@ def test_context_window_strips_provider_prefix() -> None:
     assert context_budget.context_window("openai/gpt-4o") == 128_000
 
 
+def test_context_window_chatgpt_prefix_skips_provider_auth(
+    monkeypatch: pytest.MonkeyPatch,
+) -> None:
+    context_budget._model_info.cache_clear()
+    calls: list[str] = []
+
+    def _model_info(model: str) -> dict[str, int]:
+        calls.append(model)
+        return {"max_input_tokens": 1_050_000, "max_output_tokens": 128_000}
+
+    monkeypatch.setattr("strix.llm.context_budget.litellm.get_model_info", _model_info)
+    try:
+        assert context_budget.context_window("chatgpt/gpt-5.6-luna") == 1_050_000
+        assert calls == ["gpt-5.6-luna"]
+    finally:
+        context_budget._model_info.cache_clear()
+
+
 def test_context_window_unmapped_uses_fallback(monkeypatch: pytest.MonkeyPatch) -> None:
     context_budget._model_info.cache_clear()