Adding toolsets should auto-enable the underlying tools

[digitarald]

1. Added a new research toolset that combines "perplexity_ask", "fetch".
2. Enable ONLY research in the tool picker
3. Add research via Add Context to a prompt
4. 🐛 Broken tool calling as the tools are mentioned and the AI believes they exist and keeps trying to use them

Originally reported via https://x.com/camsoft2000/status/1933502622637412522

Agent mode in Claude prints XML-based tool calls:

By accident I also did this in Ask mode, which totally throws Ask mode off; now that