fix: preserve live thinking config

[he-yufeng]

Summary

• copy GenerateContentConfig.thinking_config into the Gemini live connect config
• keep existing live connection behavior for headers, system instruction, and tools
• add a regression test that verifies aio.live.connect() receives the thinking config

To verify

• uv run pytest tests/unittests/models/test_google_llm.py -q
• uv run pyink --check src/google/adk/models/google_llm.py tests/unittests/models/test_google_llm.py
• python -m py_compile C:\dev\GITHUB-clean\adk-python\src\google\adk\models\google_llm.py C:\dev\GITHUB-clean\adk-python\tests\unittests\models\test_google_llm.py
• git diff --check -- src/google/adk/models/google_llm.py tests/unittests/models/test_google_llm.py

Fixes #5805

[adk-bot]

Response from ADK Triaging Agent

Hello @he-yufeng, thank you for creating this PR!

This PR is a bug fix, and while you have provided a detailed "To verify" section, could you please also:

• Provide a summary of the passed pytest results as per our unit testing guidelines.
• Provide logs or screenshots after the fix is applied (where applicable) to help reviewers understand and verify the fix more easily.

This information will help our reviewers review your PR more efficiently. Thanks!

[he-yufeng]

Rebased this branch onto current upstream/main and re-ran the focused checks.

Validation on Windows:

uv run --no-sync pytest tests/unittests/models/test_google_llm.py::test_connect_copies_thinking_config_to_live_config -q --basetemp .tmp\pytest -p no:cacheprovider
# 1 passed

uv run --no-sync pytest tests/unittests/models/test_google_llm.py -q --basetemp .tmp\pytest -p no:cacheprovider
# 62 passed, 3 warnings

uv run --no-sync pyink --check src/google/adk/models/google_llm.py tests/unittests/models/test_google_llm.py
uv run --no-sync python -m py_compile src/google/adk/models/google_llm.py tests/unittests/models/test_google_llm.py
git diff --check upstream/main...HEAD

The warnings are the existing experimental feature warnings from this test file.

[he-yufeng]

Rebased onto current main again; no code changes beyond the rebase.\n\nValidation on Windows:\n- uv run --no-sync pytest tests\unittests\models\test_google_llm.py::test_connect_copies_thinking_config_to_live_config -q --basetemp .tmp\pytest-5812-20260524 -p no:cacheprovider -> 1 passed\n- uv run --no-sync pytest tests\unittests\models\test_google_llm.py -q --basetemp .tmp\pytest-5812-full-20260524 -p no:cacheprovider -> 62 passed, 3 existing experimental warnings\n- uv run --no-sync pyink --check src\google\adk\models\google_llm.py tests\unittests\models\test_google_llm.py\n- uv run --no-sync python -m py_compile src\google\adk\models\google_llm.py tests\unittests\models\test_google_llm.py\n- git diff --check upstream/main..HEAD