Can we only use the supavisor connection pooler with the default `postgres` database?

Even if I provide the db to the pooler connection string (a different DB that I added myself via prisma so that it is private and I don't need to manage RLS) it seems like when I make requests to the pooler it does not find the tables (ie. its not going to the db that I specified), but if I change it to a direct connection string then it does.