Two ways to use Supabase. The first is the one that gets first class citizen status is their API. Never used it, seems way too complicated but maybe useful if you can do full SQL on the back end and use the API to serve JSON to your end points where SQL is not practical or available.
Second is standard database connection like any other, they do hide the settings you need for that and I have to go hunting every time.
Got to Settings...Database and then scroll down to fid the connection info.
Edit: I use pgAdmin to create the tables, indexes, queries, manage dataand such even though most of that can be done in the Supabase website. It's what I know and is more powerful and flexible. You could can also use Retool Grid (in beta still I believe) to do all of that.