docs: add a runnable chat room example

[electrohyun]

Summary

Adds examples/, outside the published package, with the minimal chat room from #113. One room, two clients, one broadcast, plus an example README saying what it demonstrates. examples/* joins the pnpm workspace so the example resolves smocket by workspace link, and pnpm example:chat-room builds and runs it in one command.

Verified from a clean clone: pnpm install --frozen-lockfile then pnpm example:chat-room prints the output the example README quotes, and it is stable across runs because both joins are acknowledged before anyone speaks.

The larger application example in #113 is not here. It is recovered from the dogfooding application, which does not exist yet, and so are the browser sandbox link and the scaffolding command that reach these files.

Related issue

Part of #113

Checklist

• Tests added or updated
• Behavior verified against real socket.io

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Review details

⚙️ Run configuration

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Review profile: CHILL

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Run ID: 7c97837f-ae70-4935-8b00-65cd6f00eaed

📥 Commits

Reviewing files that changed from the base of the PR and between ac3daf3 and 5963cb9.

⛔ Files ignored due to path filters (1)

• pnpm-lock.yaml is excluded by !**/pnpm-lock.yaml, !pnpm-lock.yaml

📒 Files selected for processing (7)

• .github/workflows/ci.yml
• README.md
• examples/chat-room/README.md
• examples/chat-room/index.js
• examples/chat-room/package.json
• package.json
• pnpm-workspace.yaml

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