To cover your list:
- Auth: Supabase has auth, with oauth support for many services. Also prebuild UI for login forms etc. It's really easy to set up
- Live updates: Supabase has a realtime api to send messages, or subscribe to db changes
- Database: Supabase is basically a Postgres database with a bunch of stuff on top, it generates a REST/GraphQL api from your schema, meaning you don't have to make endpoints.
It's incredibly productive as it covers all the basics. It's open source so you are not locked in, and they have a free plan that will get you quite far.
For the frontend Next.js is my preference, but you could opt for other frameworks if you are more familiar with them. Next.js on Vercel is really easy to set up with preview builds, automatic deployments etc.