### Check for existing issues

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

### What happened?

Web search interception doesn't work with OpenAI provider when `stream: true`. I would expect it to work the same way it does with `stream: false`

### Steps to Reproduce

1. Configure search tool & web_search interception as per https://docs.litellm.ai/docs/integrations/websearch_interception 2. Test interception works when `stream=false` ``` curl -X 'POST' \ 'https://{litellm-host}/v1/chat/completions' \ -H 'accept: application/json' \ -H 'x-litellm-api-key: sk-XXXXXX' \ -H 'Content-Type: application/json' \ -d '{ "model": "openai-gpt-5.1", "messages": [ { "role": "user", "content": "What is the weather in San Francisco today?" } ], "tools": [ { "type": "function", "function": { "name": "litellm_web_search", "description": "Search the web for information, always include URL in citations", "parameters": { "type": "object", "properties": { "query": { "type": "string" } }, "required": [ …