#32505 fix(anthropic_responses): translate_tool_choice_to_responses_api returns invalid objects instead of string literals
## Bug
`translate_tool_choice_to_responses_api` in the Anthropic→Responses API adapter returns `{"type": "auto"}` and `{"type": "required"}` (object form) where the OpenAI Responses API requires string literals `"auto"` and `"required"`. This causes 400/422 errors from vLLM (and potentially other OpenAI-compatible backends) when an Anthropic `/v1/messages` client sends `tool_choice` and the request is routed through the Responses API path.
## What happened
LiteLLM v1.91.0 proxy receiving Anthropic `/v1/messages` requests for an `openai/`-provider model (e.g. vLLM backend) routes through the Responses API adapter (`litellm/llms/anthropic/experimental_pass_through/responses_adapters/`). The `tool_choice` translation produces invalid objects:
| Anthropic `tool_choice` | Current output (broken) | Correct output | |---|---|---| | `{"type": "auto"}` | `{"type": "auto"}` | `"auto"` | | `{"type": "any"}` | `{"type": "required"}` | `"required"` | | `{"type": "none"}` | `{"type": "auto"}` ← **also wrong: enables tools when user asked to disable** | `"none"` | | `{"type": "tool", "name": "foo"}` | `{"type": "function", "name": "foo"}` | `{"type": "function", "name": "foo"}` (correct alrea…