Backup recovery in a small, simple, robust system is very rare. Automated recovery is complex and there are quite a bunch of gotchas and perhaps project specific things to take into account.
But automated backups are typically straightforward. You need to know when and how to do them and where to put them.
I think there are tons of reasons to pay for an managed database if you need it. But it is not a baseline requirement for many projects.
For managed, I don't think I'd want to go lower than the $50 plan which would be roughly equivalent to what I have now.. would include storage but not backups I think.
But ya the data is valuable.. I'm running nightly backups. I want to do continuous backups someday or have some way to not lose up to 24 hours of data if something happens.