fix(python/google-ai): skip api_key check when use_vertexai is True

The api_key validation in GoogleAIChatCompletion, GoogleAITextCompletion,
and GoogleAITextEmbedding ran unconditionally, blocking Vertex AI users
who authenticate via Application Default Credentials (no API key).

Guard the check with `not google_ai_settings.use_vertexai` so that only
non-Vertex AI configurations require an API key.  The error message
already reads 'when use_vertexai is False', matching the new condition.

Fixes #13483

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

Author: giulio-leone

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/semantic_kernel/connectors/ai/google/google_ai/services/google_ai_text_completion.py

@@ -90,7 +90,7 @@ 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/semantic_kernel/connectors/ai/google/google_ai/services/google_ai_text_embedding.py

@@ -81,7 +81,7 @@ 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__(