hopefully this helps. my postgresAdapter has a few other values

db: postgresAdapter({
pool: {
  connectionString: process.env.DATABASE_URI || "",
  max: 10,
  min: 2,
  idleTimeoutMillis: 30000,
  connectionTimeoutMillis: 2000,
},
schemaName: "someSchemaName",
}),

You can set the schema like in the image here, click on the dropdown and the last option let's you create a new one. supabase schemas

Cheers! 👋🏼