### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### What happened?

/v1/responses bridged to a non-OpenAI backend (Anthropic) fails on the follow-up turn of any tool-calling conversation:

litellm.BadRequestError: Unable to create messages for completion request. 1) Using previous_response_id without a session database, AND 2) Input contains only function_call_output with empty or invalid call_id. Original request: previous_response_id=resp_1a8d95c2-0000-4381-0000-a67dde1347a4 With store_prompts_in_spend_logs: true and Postgres backed, inspection of LiteLLM_SpendLogs reveals three independent defects

1 - request_id namespace mismatch. Bridge translates Responses API to Chat Completions internally and stores chatcmpl-<uuid> in request_id, but returns resp_<uuid> to the client. ResponsesSessionHandler.get_chat_completion_message_history_for_previous_response_id() queries WHERE request_id = $1 with the decoded resp_<uuid> - no match - reconstruction returns empty.

2 - messages column = {} for aresponses call_type. Even with store_prompts_in_spend_logs: true, only response is persisted. messages is an empty obje…