This was true for RDS serverless v1 which scaled to 0 but is no longer offered. V2 requires a minimum 0.5 ACU hourly commit ($40+ /mo).
https://aws.amazon.com/blogs/database/introducing-scaling-to...
It only scales down after a period of inactivity though - it’s not pay-per-request like other serverless offerings. DSQL looks to be more cost effective for small projects if you can deal with the deviations from Postgres.