I think people tend to overthink about running your own db.
There is nothing to patch manually. Security updates are handled automatically via "unattended-upgrades" for Ubuntu and when the OP says,
> tiny, almost free, sql database for personal projects
running "mysqldump" on a cron job sounds enough to me.
> with reasonable disaster recovery
You may send that dump file to any S3 based storage anywhere in the world for a decent disaster recovery. (Tools like restic allows automatic data rotation easily.)
Launching an instance (even use "MySQL" app instance cloud providers provide) and installing MySQL with 1 command, write a few lines of shell script to take a daily backup should take at most an hour.
Optionally, install Caddy web server and set up a few lines for PHP fpm or for other languages a single line to reverse proxy for automatic Let's Encrypt and your site is up. I'm sure there are plenty of tutorials on that.
Once things are up, there's nothing to manage. It gives you flexibility with lower price, not to mention gives you the little knowledge you likely want to have down the road.