Disabling Web Search is not respected if it was previously active during the same chat

[marksftw]

1. Make a new chat with web search on. "Weather in Austin"
2. After results, in same chat, turn web search off and search "Weather in San Francisco".
3. Chat still uses web search.

Expected behavior: web search is not available.
Actually behavior: web search tool is still available despite being deactivated.

It's possible this is a technical decision and is known.

The opposite case works differently. If a new chat starts with web search off, correctly does not have tool available. In same chat, turn web search on and the web search tool becomes available to the user as expected.