Earlier quoted context omitted.
I'd argue just find a different cloud provider. GCP, Azure, Supabase, Cloudflare etc if you want managed services. If you want a mix of managed services and raw compute, look more at Fly.io, Linode, Digital Ocean perhaps? I have found AWS being the "cheapest" or even "reasonable" in the cost department to be slimmer every year.
Cloudflare doesn’t let you host Docker containers or offer managed Postgres do they?
I just listed managed services (not all of them may fit I imagined)