You can force NOT whatever web_search is being mapped to on your org or project as an alias or pointer when you explicitly state a version, only seen documented in the API reference:
"tools":[{ "type": "web_search_2025_08_26" }]
web_search_preview is 2025_03_11, BTW, the date of the Responses API release. It doesn’t support a URL whitelist, the source citation, and also likely doesn’t confer a lower price now offered.
I would not “force” any internal tool. One bug, or the AI actually being forced, and you will get max tool calls with no return.