How to deploy Supabase MCP server on Vercel

I have an expense tracker app in Next.js that uses Supabase for auth and database services. I want to add a feature to query my database in natural language with the help of the Supabase MCP server and an LLM (Gemini in this case). I want to deploy the Supabase MCP server tools on Vercel, but want to clarify some things.

The Vercel documentation for mcp-adapter shows how to deploy custom tools - but the Supabase MCP server already has all the tool definitions. So my question is, how do I deploy a Supabase MCP server on Vercel? Do I have to copy-paste tool definitions from the Supabase MCP server documentation into my “server code script” that gets deployed on vercel? Or is there a better way to do this?

Here are some links for more context -

I am still a beginner trying to upskill myself, so any help is appreciated!