feat: add you.com search provider

[mouse-value-add]

Hi maintainers, thanks for building dart_agent_core, it is a great fit for practical tool-using agents in Flutter and Dart environments.

I picked this repo because it is an agent runtime where web search is a natural tool dependency, and there was not yet a first-party You.com Search integration example.

What changed

• Added
  • Implements a tool using
  • Supports optional via env var
  • Includes fallback/error handling for empty query, non-200 API response, and no-result cases
• Updated with a short section showing where the You.com example lives and how to run it.

Setup

1. Export (required for the LLM client in the example)
2. Optionally export (Search API also supports a free no-key tier up to daily limit)

3. Run:

Validation

• Confirmed code compiles logically with existing project dependencies ( is already present).
• Tried running tests, but is not installed in my current execution environment, so I could not execute here.

Why this helps agent intelligence

This adds a clean, low-risk way for agents built with this framework to perform live web lookup for factual grounding, while keeping implementation small and easy to maintain.

Backward compatibility is preserved: this is additive (new example + docs only), with no behavior changes to existing APIs.

Happy to adjust naming, example style, or placement if you prefer a different project convention.