### Check for existing issues

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

### What happened?

When using the LiteLLM proxy with Vertex AI (Gemini), sending a request from codex cli that includes both function calling tools and web_search_options causes a 400 error: "Multiple tools are supported only when they are all search tools"

Root cause: LiteLLM converts the web_search Responses API tool into web_search_options before the Vertex AI mapper runs. The tools parameter (function declarations) and web_search_options are then mapped independently. _resolve_search_tool_conflict only runs inside _map_function and never sees the googleSearch Tool added by _map_web_search_options, so the conflict is never caught

### Steps to Reproduce

1. Send a chat completion request to a Vertex AI Gemini model with both: - tools: [{ type: "function", function: { name: "my_func", ... } }] - web_search_options: {} …