"vastly superior to self hosting regarding observability" I'd suggest looking into the cnpg operator for Postgres on Kubernetes. The builtin metrics and official dashboard is vastly superior to what I get from Cloudwatch for my RDS clusters. And the backup mechanism using Barman for database snapshots and WAL backups is vastly superior to AWS DMS or AWS's disk snapshots which aren't portable to a system outside of AWS if you care about avoiding vendor lock-in.
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.
Right now from Hetzner you can get a dedicated server with 6c/12t Ryzen2 3600, 64GB RAM and 2x512GB Nvme SSD for €37/mo
Even if you just served files from disc, no RAM, that could give 200k small files per second.
From RAM, and with 6 dedicated cores, network will saturate long before you hit compute limits on any reasonably efficient web framework.
There is no reason to self manage pg for dev / environnement.
https://aws.amazon.com/rds/aurora/serverless/