even if the free tier is exhausted, their 1GB disk development PostgreSQL when billed is $2.09 per month. that's cheap.
Development - Single node, 1x shared CPU, 256MB RAM, 1GB disk
https://fly.io/docs/about/pricing/#postgresql-clusters https://fly.io/docs/reference/postgres/
There's also https://railway.app/ too. I find their free tier incredibly generous and I am using their managed postgres instance for my side projects
(I am not affiliated)
https://fly.io/docs/about/pricing/