studio/backend: fix backend CI failures for providers router

- test_desktop_auth: include providers_router in the routes stub so
  studio.backend.main imports cleanly under the monkeypatched module
- test_providers_api: skip the whole module when STUDIO_TEST_PASSWORD
  is unset (it is an integration test against a live Studio server,
  same shape as the already-ignored test_studio_api.py)

studio/backend/tests/test_desktop_auth.py

@@ -383,6 +383,7 @@ def test_health_response_reports_desktop_capability_fields(monkeypatch):
         inference_router = APIRouter(),
         inference_studio_router = APIRouter(),
         models_router = APIRouter(),
+        providers_router = APIRouter(),
         training_history_router = APIRouter(),
         training_router = APIRouter(),
     )

studio/backend/tests/test_providers_api.py

@@ -38,6 +38,14 @@ BASE_URL = os.getenv("STUDIO_TEST_URL", "http://localhost:8000")
 USERNAME = os.getenv("STUDIO_TEST_USER", "unsloth")
 PASSWORD = os.getenv("STUDIO_TEST_PASSWORD", "")
 
+# These tests require a live Studio server reachable at BASE_URL with a known
+# bootstrap password. Skip the whole module when that environment is missing
+# (e.g. on CI runners) so pytest discovery does not error out.
+pytestmark = pytest.mark.skipif(
+    not PASSWORD,
+    reason = "Integration test requires a running Studio server; set STUDIO_TEST_PASSWORD to enable.",
+)
+
 # Map provider_type → (env var name, model to use for inference test)
 _PROVIDER_CONFIGS: dict[str, tuple[str, str]] = {
     "openai": ("OPENAI_API_KEY", "gpt-4o-mini"),