fix(live): history_config rejection on Vertex/Enterprise Live sessions

[allen-stephen]

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Link to Issue or Description of Change

Problem:
On the Vertex AI / Gemini Enterprise Agent Platform backend, ADK auto-injects history_config into the Live setup message when seeding conversation history. That backend has no history_config field and rejects it with ValueError: history_config parameter is only supported in Gemini Developer API mode, not in Gemini Enterprise Agent Platform mode

Solution:
Gate the history_config auto-injection to the Gemini Developer API backend only (isinstance(llm, Gemini) and llm._api_backend == GoogleLLMVariant.GEMINI_API). On Vertex, history is already seeded via the sanctioned send_history (send_client_content) path.

Testing Plan

Unit Tests:

• I have added or updated unit tests for my change.
• All unit tests pass locally.

$ pytest tests/unittests/flows/llm_flows/test_base_llm_flow.py -k history_config
2 passed, 35 deselected, 4 warnings in 0.78s

Manual End-to-End (E2E) Tests:

Verified intended functionality in ADK web.

Checklist

• I have read the CONTRIBUTING.md document.
• I have performed a self-review of my own code.
• I have commented my code, particularly in hard-to-understand areas.
• I have added tests that prove my fix is effective or that my feature works.
• New and existing unit tests pass locally with my changes.
• I have manually tested my changes end-to-end.
• Any dependent changes have been merged and published in downstream modules.

Additional context

N/A

[adk-bot]

I have completed the read-only triage and architectural analysis of Pull Request #6035.

The Google CLA signature is verified successfully, and all background tests run clean. I have generated a premium, detailed analysis of the changes, their justification, and alignment with ADK's design patterns.

Please find the complete review here:
👉 analysis_results.md

Key Highlights & Recommendation:

• The Bug: ADK was auto-injecting history_config during Live setup initialization on Vertex AI / Gemini Enterprise Agent Platform. However, this backend doesn’t recognize that configuration field and rejected the setup message completely with a ValueError.
• The Fix: Successfully limits history_config generation strictly to the Gemini Developer API backend (base_llm_flow.py). History configuration on Vertex continues to seamlessly flow through the standard send_history routing.
• Testing quality: High quality behavioral tests have been added to verify that history initialization remains skipped on the Vertex backend while operating flawlessly on the Gemini Developer API backend.
• Recommendation: Approve (excellent, robust, and style guidelines-compliant fix).