### Check for existing issues

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

## What happened?

When using Claude Code through LiteLLM Proxy with a `hosted_vllm` model and `websearch_interception` enabled, Claude Code native WebSearch requests can be short-circuited before the request reaches the vLLM model.

In this flow, LiteLLM runs the configured search provider, for example Serper, and returns formatted search results directly as a synthetic Anthropic Messages response. The vLLM model never receives the search results as tool output, so it cannot synthesize a final answer.

In some cases the returned response is also text-only, without the native Anthropic web-search blocks (`server_tool_use` and `web_search_tool_result`) that Claude Code expects for WebSearch accounting/citation handling.

Expected flow: ```mermaid sequenceDiagram participant CC as Claude Code participant LL as LiteLLM Proxy participant V as vLLM Model participant S as Serper.dev

CC->>LL: /v1/messages with WebSearch tool LL->>V: Ask model what to search V-->>LL: Tool call / search query LL->>S: Search web S-->>LL: Search results LL->>V: Feed resu…