For a serverless, the cost is very much "it depends". Serverless is great if you only use the database occasionally and you can accept that the few times you access it, it takes some time to start it. As long as the database is rolled out, you only pay for storage. You only pay for compute when it is loaded. This also mean that the actual cost depends very much on your usage pattern.
Having a serverless database which is active all the time is a lousy idea of the simple reason that it is more expensive than a provisioned database.