fix(responses): store complete assistant response in Redis sessions

[josemaria-vilaplana]

Summary

• Fix multi-turn conversations with Gemini thinking models (2.5/3) when using tool calling via the Responses API
• Previously, Redis session storage only stored input messages, missing the assistant response with tool_calls and provider_specific_fields
• This caused "Base64 decoding failed for thought_signature" errors on follow-up requests

Changes

• Extract and store complete assistant message including tool_calls in Redis sessions
• Preserve provider_specific_fields containing thought_signatures (critical for Gemini thinking models)
• Handle both streaming and non-streaming response paths
• Add comprehensive tests for thought_signature preservation (17 new tests)

Test plan

• Run unit tests: pytest tests/test_litellm/responses/litellm_completion_transformation/test_thought_signature_preservation.py (17 passed)
• Run related tests: pytest tests/test_litellm/responses/litellm_completion_transformation/ (98 passed, 1 skipped due to missing dependency)
• Manual test with Gemini 2.5/3 thinking model + tool calling + multi-turn conversation

🤖 Generated with Claude Code

[mateo-di]

@josemaria-vilaplana can we check if we have a test already that verify this carto-customization in the smoke-ai tests in cloud-native?

[josemaria-vilaplana]

@josemaria-vilaplana can we check if we have a test already that verify this carto-customization in the smoke-ai tests in cloud-native?

No way we can test this with our current tests approach. This fails randomly, only when the thought_signatures in base64 is bigger then 2K, which happens only from time to time depending on the encoded value.