Add support for new Responses API and web search

[LizzyG]

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Is your feature request related to a problem? Please describe.
I'm able to call the normal ChatCompletionRequest with an array of tools, however I'm not able to use the built in web_search tool that was announced with the Responses API this week.

Describe the solution you'd like
I'd like to be able to specify the built in web_search_preview tool along with my custom tools.

Describe alternatives you've considered
I tried putting web_search_preview as the name of a tool but that failed. I tried specifying it in my prompt, that also did not work.

Additional context
I'm currently using the ChatCompletionRequest with custom tools and ideally I'd like to be able to just add on web search without migrating to a new Responses specific type since I don't need the managed context. But I'm happy to migrate to a new ResponsesRequest or whatever to get web search capability.

[LizzyG]

Looks like i can probably use model gpt-4o-mini-search-preview model with tool calling via prompt. Would still like Responses API for context maintenance but my specific use case can be managed as-is.

[robfig]

Looks like using the web-search model is not as good, because it forces its use on every request.

From https://platform.openai.com/docs/guides/tools-web-search?api-mode=chat

When using Chat Completions, the model always retrieves information from the web before responding to your query. To use web_search_preview as a tool that models like gpt-4o and gpt-4o-mini invoke only when necessary, switch to using the Responses API.

[gy-mate]

using the web-search model is not as good, because it forces its use on every request.

You mean using the gpt-4o-search-preview model with the Responses API? Yeah, resolving this GitHub issue would solve that problem.