Refactor auth example from `next-auth` to Supabase Auth.

[en3sis]

📝 Is your feature request related to a problem? Please describe.

Since Supabase already provides a robust auth system with plenty of providers, we want to change the default auth configuration from the Next-Auth to Supabase

💠 Describe the solution you'd like

• Clean up the current implementation of the next-auth & GitHub provider.
• Implement the https://supabase.com/docs/guides/auth/auth-helpers/nextjs example.

🔆 Additional context