### Check for existing issues

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

### What happened?

**Title** OpenAI Responses adapter converts Anthropic `thinking` blocks to `output_text` when replaying message history

**Summary** When using `anthropic_messages()` with an OpenAI model, prior assistant `thinking` blocks in the conversation history are serialized into regular `output_text` blocks instead of reasoning blocks.

This causes hidden/internal thinking content returned by LiteLLM as an Anthropic-style `thinking` block to be sent back to OpenAI as normal assistant-visible text on the next request.

**Expected Behavior** An Anthropic-style assistant content block like:

```python {"type": "thinking", "thinking": "...", "signature": ""} ```

should either:

1. Be converted into the appropriate OpenAI Responses reasoning representation, or 2. Be omitted/redacted from the next OpenAI request (I think this was done in `1.81.x` versions)

It should not be sent as regular assistant text.

**Actual Behavior** LiteLLM serializes the `thinking` block as:

```json { "type": "output_text", "text": "**THINKING MESSAGE**" } ```

inside the ass…