I’m not against AWS or $36/mo. It just is kinda a drag when the promise of serverless is pay per user and scaling to zero. You could get a nice EC2 t3.medium and do a lot more RPS for the cost of that NAT and Lambda invocations.
If you don’t care about cold starts, there is always Aurora Serverless with the Data API. I don’t believe it requires either a NAT or for the lambda to be attached to your VPC.