refactor(ai_client): migrate L1594 _list_gemini_models to Result[T] (Phase 10 site 1)

The original function had a broken pattern: 'raise _classify_gemini_error(exc)
from exc' which raises an ErrorInfo (not an Exception) — a runtime bug.

Per TIER1_REVIEW 2026-06-20 directive: per-site decision. The body raised a
structured error carrier (ErrorInfo), but the pattern was incorrect (ErrorInfo
is not an Exception). Cleanest fix: full Result[T] migration.

New helper:
- _list_gemini_models_result(api_key: str) -> Result[list[str]]
  Returns Result(data=sorted_models) on success, Result(data=[], errors=[ErrorInfo])
  on SDK/network failure.

Legacy wrapper:
- _list_gemini_models(api_key: str) -> list[str]
  Returns result.data (preserves original signature; callers don't see errors).

Audit: ai_client BC 9 -> 8. Site L1594 (now shifted to L1609 due to helper insertion)
no longer in INTERNAL_BROAD_CATCH.

tests/tier2/phase10_site1_test.py

@@ -0,0 +1,37 @@
+"""Phase 10 invariant tests (RED).
+
+Site 1 (L1594): _list_gemini_models_result helper must exist + return Result[list[str]].
+"""
+import sys
+sys.path.insert(0, ".")
+
+from src.result_types import Result, ErrorInfo
+
+
+def test_phase10_site1_list_gemini_models_result_exists():
+    import src.ai_client
+    assert hasattr(src.ai_client, "_list_gemini_models_result"), \
+        "_list_gemini_models_result helper missing from src.ai_client"
+
+
+def test_phase10_site1_list_gemini_models_result_returns_result():
+    """The helper must return a Result[list[str]]."""
+    import src.ai_client
+    fn = getattr(src.ai_client, "_list_gemini_models_result", None)
+    assert fn is not None
+    import inspect
+    sig = inspect.signature(fn)
+    # Should have a return annotation of Result
+    assert "Result" in str(sig.return_annotation), \
+        f"_list_gemini_models_result return annotation must be Result, got {sig.return_annotation}"
+
+
+def test_phase10_site1_list_gemini_models_legacy_unchanged():
+    """Legacy _list_gemini_models must still return list[str] (preserve signature)."""
+    import src.ai_client
+    fn = getattr(src.ai_client, "_list_gemini_models", None)
+    assert fn is not None
+    import inspect
+    sig = inspect.signature(fn)
+    assert "list[str]" in str(sig.return_annotation) or "list" in str(sig.return_annotation), \
+        f"_list_gemini_models return annotation must remain list[str], got {sig.return_annotation}"