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Describe the bug
When deployed to Cloud Run with MySQL database as the session store, the ADK app encountered issues when the end user double texts, i.e. the user sends multiple messages while the agent is thinking.

There is not encountered when it is locally deployed using in memory session.

To Reproduce

1. Deploy the ADK agent to Cloud Run
2. Configure to use the MySQL Session Store
3. Sends multiple messages while the agent is thinking

Expected behavior
The agent handles the messages one by one in order without errors

Logs
Traceback (most recent call last):\n File "/usr/local/lib/python3.13/site-packages/google/adk/cli/fast_api.py", line 697, in event_generator\n async for event in runner.run_async(

ERROR:google_adk.google.adk.cli.fast_api:Error in event_generator: The last_update_time provided in the session object '2025-05-30 08:19:13' is earlier than the update_time in the storage_session '2025-05-30 08:19:14'. Please check if it is a stale session.

Desktop (please complete the following information):

• Platform: Cloud Run
• Python version(python -V): 3.11.12
• ADK version(pip show google-adk): 1.0