cnippet-dev/ui-cnippet — reverse-engineered prompt

Build me a polished website and component library for Cnippet UI. I want it to feel like a modern shadcn style experience, but using Base UI with Tailwind CSS v4. The main goal is a docs site where people can browse accessible React components, preview them, copy paste the code, and quickly add either one component or the whole set into their app.

Please include a solid set of components across actions, forms, overlays, navigation, data display, layout, feedback, and pickers, with examples like buttons, inputs, dialogs, tables, charts, tabs, menus, calendar, select, toast, tooltip, and more. Make the docs clear and friendly, with install snippets, usage examples, styling tokens, theming notes, and migration help for people coming from shadcn/ui or Radix style components.

I also want the project to feel production ready, accessible, cleanly organized, and easy for AI tools to understand and extend. A docs home page, component detail pages, and a simple live demo or playground would be great. Look up current docs online if you need to.