BadRequestError: tool_call_id not found when using Claude/OpenAI with session history containing tool calls

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Describe the Bug:
When using Claude via Vertex AI or OpenAI models with ADK, replaying session history that contains tool calls results in a BadRequestError because tool_call_id is missing.

Steps to Reproduce:

1. Use ADK with session continuity (loading previous session events)
2. The previous session contains tool calls (function_call and function_response)
3. Use Claude via Vertex AI or the OpenAI model via LiteLLM
4. Send a follow-up message that requires replaying the session history

Root Cause Analysis

1. Gemini API returns id=None for function calls
2. ADK's populate_client_function_call_id() generates adk-{uuid} IDs to fill this gap
3. Before sending history to LLM, remove_client_function_call_id() strips all adk-* prefixed IDs, setting them to None
4. Claude via Vertex AI and OpenAI requires tool_call_id on tool response messages to match them to function calls
5. With IDs stripped, these models fail with BadRequestError

Expected Behavior:
Session history with tool calls should work correctly with Claude/OpenAI models. The adk-* function call IDs should be preserved since:

• Claude via Vertex AI requires tool_call_id
• OpenAI models require a matching tool_call_id
• Gemini ignores extra IDs (generates its own or uses None)

Observed Behavior:
What actually happened? Include error messages or crash stack traces here.

Environment Details:

• ADK version: 1.2.3+
• Python version: 3.11
• Model: Claude via Vertex AI (also affects OpenAI via LiteLLM)

Model Information:

• Are you using LiteLLM: Yes
• Which model is being used: Claude via Vertex AI (also affects OpenAI via LiteLLM)

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Regression:
Did this work in a previous version of ADK? If so, which one? No

Logs:
Please attach relevant logs. Wrap them in code blocks (```) or attach a
text file.

litellm.BadRequestError: litellm.BadRequestError: VertexAIException BadRequestError - 
{'error': {'message': "tool_call_id '...' not found in list of function calls in the chat history"}}

How often has this issue occurred?:

• Always (100%)