fix(antigravity): add web search tool support for Claude/OpenAI format requests

[adrenjc]

Summary

This PR fixes a critical user experience bug where web_search tool requests via Claude/OpenAI API formats are silently ignored by the Antigravity backend.

Problem

This is a severe UX issue that completely breaks web search functionality.

Current behavior:

• When users send {"type": "web_search"} tool via Claude API format → tool is silently ignored
• When users send {"type": "web_search"} tool via OpenAI API format → also ignored
• Even when Gemini backend returns grounding results (groundingMetadata) → response data is completely lost, client sees nothing

From user's perspective: They configure web search tool, but AI never searches and never returns any citations. Users assume the feature is broken or disabled.

Solution

Request Translation

• Detect Claude format {"type": "web_search"} or {"name": "web_search"} tool declarations
• Detect OpenAI format {"type": "web_search"} tool declarations
• Convert to Gemini's {"googleSearch": {}} format
• Auto-set requestType: "web_search" flag
• Force use gemini-2.5-flash model (currently the only model supporting grounding)

Response Translation

• Parse groundingMetadata.webSearchQueries and groundingMetadata.groundingChunks from Gemini response
• Convert to Claude format server_tool_use + web_search_tool_result content blocks
• Support both streaming (SSE) and non-streaming responses

Changed Files

File	Change
antigravity_executor.go	Add requestType detection, auto-identify web_search requests
antigravity_claude_request.go	Claude → Antigravity request conversion, detect web_search tool
antigravity_claude_response.go	Antigravity → Claude response conversion, extract and format search results
antigravity_gemini_request.go	Gemini → Antigravity request conversion, set requestType
antigravity_openai_request.go	OpenAI Chat → Antigravity request conversion
antigravity_openai-responses_request.go	OpenAI Responses → Antigravity request conversion

Screenshots

Before

After

Note: This PR includes commit 9c0e746 from #1126 (pending merge).

Testing

• Claude format web_search tool request → correctly converted and returns search results
• OpenAI format web_search tool request → correctly converted and returns search results
• Streaming response correctly outputs server_tool_use and web_search_tool_result events
• Non-streaming response correctly contains search result blocks

[hkfires]

I'm sorry, but our project only acts as a message carrier/forwarder, and we currently have no plans to implement specific functionality by using a redirection model.