Free tier gives you a ton of usage across most of the services, but definitely not enough to fully host a side project. But e.g. you can use RDS (database hosting), S3, EC2, text to speech and do whatever you want in a small scale for a year. It's kind of enough to learn for certificates.

I forgot to remove NAT Gateway for a few weeks while learning bits and pieces of VPC usage and it ended up costing me 25$... what can you do.

You're probably still not that customer. You're still concerned about your own money, vs spending employers' money.