### Check for existing issues

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

### What happened?

When the Anthropic `/v1/messages` experimental adapter proxies a **multi-turn, tool-using** conversation to an **OpenAI-compatible reasoning backend** (vLLM/SGLang serving a DeepSeek "thinking" model), the assistant degenerates into **phrase repetition** that **grows with conversation length**:

``` Continuing. Continuing. Continuing. ```

It is invisible on short conversations and only appears once the history is long (≈8+ tool turns). The streamed SSE is well-formed - no error, no fallback - the model genuinely generates the repeated tokens.

**Root cause.** `LiteLLMAnthropicMessagesAdapter.translate_anthropic_messages_to_openai` (`litellm/llms/anthropic/experimental_pass_through/adapters/transformation.py`) attaches the `thinking_blocks` field to **every replayed assistant turn, for every backend**:

```python assistant_message = ChatCompletionAssistantMessage( role="assistant", content=assistant_content, thinking_blocks=(thinking_blocks if len(thinking_blocks) > 0 else None), ) ... if len(thinking_blocks) > 0: assistant_mess…