Python: fix(google): allow Vertex AI usage without API key when using ADC

python/semantic_kernel/connectors/ai/google/google_ai/services/google_ai_chat_completion.py

@@ -119,7 +119,7 @@ def __init__(
         if not client:
             if google_ai_settings.use_vertexai and not google_ai_settings.cloud_project_id:
                 raise ServiceInitializationError("Project ID must be provided when use_vertexai is True.")
-            if not google_ai_settings.api_key:
+            if not google_ai_settings.use_vertexai and not google_ai_settings.api_key:
                 raise ServiceInitializationError("The API key is required when use_vertexai is False.")
 
         super().__init__(

python/tests/unit/connectors/ai/google/test_google_ai_chat_completion_vertex_adc.py

@@ -0,0 +1,22 @@
+import pytest
+
+from semantic_kernel.connectors.ai.google.google_ai.google_ai_settings import GoogleAISettings
+from semantic_kernel.connectors.ai.google.google_ai.services.google_ai_chat_completion import (
+    GoogleAIChatCompletion,
+)
+from semantic_kernel.exceptions.service_exceptions import ServiceInitializationError
+
+
+def test_vertexai_does_not_require_api_key_when_adc_is_used():
+    """
+    When use_vertexai=True, GoogleAIChatCompletion should NOT require an API key,
+    because authentication is handled via Application Default Credentials (ADC).
+    """
+
+    GoogleAIChatCompletion(
+        gemini_model_id="models/gemini-1.5-pro",
+        api_key=None,
+        use_vertexai=True,
+        project_id="test-project",
+        region="us-central1",
+    )