docs(examples): add web research example using web_search

[ben-reitz]

Summary

A new example, examples/web-research: a chat agent that answers from the live web with the web_search tool from #2502 and cites its sources. A side panel shows each search three ways: Results, Model saw (the trimmed toModelOutput text) and You got (the full response), plus settings for provider and max results.

I've also done a bunch of UI improvements compared to the other examples to remove some of the janky behaviour and improve the design. e.g. the feed only follows the stream while you're at the bottom, tool steps show a pending state between them, and the chat pieces live in a reusable src/chat-ui.tsx.

There's a ton we should probably do for all the other examples to improve the UI but this will do for now.

Evidence

Example deployed here: https://web-research-example.agents-b8a.workers.dev/

• Binding path via npm start on an account without credits (like agents): the search fails with web_search_payment_required, the UI shows it, and the model answers from memory.
• Funded account (my personal account): searches return results, and answers cite them inline.

Screenshots

These were taken running locally against my personal CF account (where I have gateway credit):

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