### What happened?

When LiteLLM Proxy receives a request on the Anthropic-native `/v1/messages` route (call_type=`anthropic_messages`), the `litellm_request` span emitted by the built-in `otel` callback is missing both `gen_ai.input.messages` and `gen_ai.output.messages`. Token counts, model, finish reasons, cost attributes etc. are all set correctly — only the prompt and completion content are absent. Tracing backends (Langfuse, Phoenix, Arize, etc.) render the trace input/output as empty.

The proxy clearly has the content in memory at success time — DEBUG logs show the system prompt and messages on the kwargs/optional_params dict, alongside `litellm_parent_otel_span: _Span(name="Received Proxy Server Request", …)`. It just isn't being put on the span for this call type.

### Reproduce

1. LiteLLM Proxy v1.88.1 (also reproduces on HEAD as of 2026-06-10) 2. `callbacks: [otel]` and env `OTEL_INSTRUMENTATION_GENAI_CAPTURE_MESSAGE_CONTENT=span_and_event` 3. A Bedrock/Anthropic/Vertex Claude model registered as `claude-*` 4. `POST /v1/messages` from Claude Code CLI or the Anthropic SDK 5. Inspect the emitted span — `gen_ai.input.messages` and `gen_ai.output.messages` are absent

### …