vercel/chatbot ? reverse-engineered prompt

Build me a full-featured AI chatbot web app. I want it to be a Next.js project, styled with a clean, modern look using shadcn/ui and Tailwind.

The main thing is a chat interface where users can sign in and have conversations with an AI. It's important that it's flexible, so let's use the Vercel AI SDK to connect to multiple model providers like OpenAI, Anthropic, and Google.

We'll also need user authentication so people can have their own accounts, and their chat history should be saved automatically. Set up a database connection for that, maybe using a serverless Postgres provider like Neon. I want this to be a solid, hackable template that I can easily deploy to Vercel and customize later.