fix: forward thinking config to live Gemini sessions

[he-yufeng]

Summary

• Forward GenerateContentConfig.thinking_config into LiveConnectConfig before opening a Gemini live session
• Preserve existing behavior when no thinking config is set
• Add a connect-level regression test for the live config handoff

Fixes #5805.

To verify

• python -m py_compile src\google\adk\models\google_llm.py tests\unittests\models\test_google_llm.py
• uv run pytest tests\unittests\models\test_google_llm.py::test_connect_forwards_thinking_config_to_live_config tests\unittests\models\test_google_llm.py::test_connect_without_custom_headers -q
• uv run pytest tests\unittests\models\test_google_llm.py -q
• uv run ruff check src\google\adk\models\google_llm.py
• git diff --check

Note: uv run ruff check src\google\adk\models\google_llm.py tests\unittests\models\test_google_llm.py reports pre-existing lint in test_google_llm.py (os unused, and an older unused connection binding). I left those unrelated lines untouched.

[he-yufeng]

Rebased onto current upstream/main. Current head is 351645a.

Validation on Windows after rebase:

• uv run --no-sync pytest tests\unittests\models\test_google_llm.py -q --basetemp .tmp\pytest-5823-20260527 -p no:cacheprovider -> 62 passed, 3 warnings
• uv run --no-sync python -m py_compile src\google\adk\models\google_llm.py tests\unittests\models\test_google_llm.py
• uv run --no-sync pyink --check src\google\adk\models\google_llm.py tests\unittests\models\test_google_llm.py
• git diff --check upstream/main...HEAD

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

[rohityan]

Hi @he-yufeng , Thank you for your contribution! We appreciate you taking the time to submit this pull request. Please fix formatting errors by running autoformat.sh

[rohityan]

Hi @he-yufeng duplicate #5812