Python: Fix Gemini client support for Gemini API and Vertex AI (#5258)

* Add Gemini and Vertex AI client support

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

* Address Gemini PR review feedback

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

* removed sample run readme part

---------

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Co-authored-by: Evan Mattson <35585003+moonbox3@users.noreply.github.com>

python/packages/gemini/samples/gemini_advanced.py

@@ -4,9 +4,9 @@
 
 Allows the model to reason through complex problems before responding.
 
-Requires the following environment variables to be set:
-- GEMINI_API_KEY
-- GEMINI_MODEL
+Requires ``GOOGLE_MODEL`` or ``GEMINI_MODEL`` and either Gemini Developer API credentials
+(``GEMINI_API_KEY`` or ``GOOGLE_API_KEY``) or Vertex AI settings
+(``GOOGLE_GENAI_USE_VERTEXAI``, ``GOOGLE_CLOUD_PROJECT``, and ``GOOGLE_CLOUD_LOCATION``).
 """
 
 import asyncio
@@ -23,10 +23,12 @@ async def main() -> None:
     """Example of extended thinking with a Python version comparison question."""
     print("=== Extended thinking ===")
 
+    # 1. Configure Gemini extended thinking for a reasoning-heavy request.
     options: GeminiChatOptions = {
         "thinking_config": ThinkingConfig(thinking_budget=2048),
     }
 
+    # 2. Create the agent with the Gemini chat client and default thinking options.
     agent = Agent(
         client=GeminiChatClient(),
         name="PythonAgent",
@@ -34,6 +36,7 @@ async def main() -> None:
         default_options=options,
     )
 
+    # 3. Stream the answer so you can see the final response as it arrives.
     query = "What new language features were introduced in Python between 3.10 and 3.14?"
     print(f"User: {query}")
     print("Agent: ", end="", flush=True)
@@ -45,3 +48,12 @@ async def main() -> None:
 
 if __name__ == "__main__":
     asyncio.run(main())
+
+"""
+Sample output:
+=== Extended thinking ===
+User: What new language features were introduced in Python between 3.10 and 3.14?
+Agent: Python 3.11 introduced exception groups and TaskGroup.
+Python 3.12 added PEP 695 type parameter syntax.
+Python 3.13-3.14 continued improving typing, performance, and developer ergonomics.
+"""