RDS - Aurora/Postgres flavor - small instance. Entire AWS bill was < $100/month to support 10k users - app load balancer

- WAF rules

- EC2 instance

- RDS

- Cloudfront

I use fargate when deploying now to get out of box management

PaaS and managed services let you trade money for time and effort - patch management, backups, security, config optimization, simplified scale-out/availability/etc. all take time, effort and skill to get right and keep running well over time. With RDS/Aurora/AzureSql/CosmosDb (and the like) you get to focus on your app/service/product instead. It all ends up being a question of how much your time (and being able to focus) are worth to you. If this is an actual business and not a hobby, and assuming market rates for your time - I believe the managed service offering ends up the cheaper option overall.

Digital ocean also offers managed db(postgres/mysql) starting at $15/month

I've used ElephantSQL before. As long as you write efficient queries (especially avoiding N+1) and choose the right data centre it's usually reasonable for a small project.