websocket: AI agent experimentation in coder/websocket

We're using `coder/websocket` as a testbed for AI agent workflows via Coder Tasks and other AI tools. The goal is to learn what works (and what doesn't) when using agents to autonomously resolve real issues.

The work involves:

- Resolving issues using AI-assisted workflows
- Documenting learnings along the way
- Creating an `AGENTS.md` that enables AI agents to create high quality contributions