If you ask barebones, that's going to get so many different answers here because everyone will have their own definition and bias. If I inherited a small game that needs a backend, I'd pick any of those backend-as-a-service options. Supabase and Firebase comes to mind.

If you pick Supabase, it's Postgres with a web api and sdk on top. Then, sure you can serialize all the game state as a jsonb record. You don't even need to deal with authentication if you don't care about isolating games.

Free tier until you make money somehow and then pay the 25/mo.