Motivation

• Provide a new Members management demo route that reproduces the target UI as a demo page in the app routing system.
• Reuse existing PUI primitive components to keep runtime cost low and follow CSS-driven variants for styling.
• Minimize custom JavaScript logic and rely on scoped CSS for layout and visual parity with the reference.

Description

• Add demo/src/routes/members.tsx containing the Members demo markup using Avatar, Badge, Button, TabList, Tab, and Table from pui.
• Wire the Members route into the router by lazy-loading it in demo/src/main.tsx and adding a /members Route.
• Add a navigation entry under Demos in demo/src/nav.tsx linking to the new Members demo.
• Add scoped demo styles to demo/src/style.css to implement the sidebar, card, tabs, table, and floating chat button visuals.

Testing

• Started the demo dev server with pnpm --dir demo dev -- --host 0.0.0.0 --port 4173, and Vite reported ready (local server start succeeded).
• Attempted an automated Playwright screenshot of http://localhost:5173/members, but the browser failed to launch / connect (Playwright errors and crashes), so no screenshot was produced.
• No unit or CI tests were executed as part of this change.

Codex Task