DigitalOcean Droplets are functionally the same things as dedicated servers, I too use dedicated machines for my own personal projects, the example should still apply to you.
Yes an absolute URL will most likely be required in your case.
No the issue shouldn’t be related to the database.
Yes I tested everything about the Strapi application when I wrote the guides and even setup test virtual machines in my local lab and on some public clouds to validate the configurations.
Relative URLs weren’t used as that would generally imply an IP address being used, and unless the Strapi instance is running on the same machine as Nginx they won’t work, in most cases (especially enterprise production instances) the Public IP address is assigned to a gateway firewall or application firewall and not the instance Strapi is running on.
I’m spinning up some droplets (effectively virtual machines) in Digital Ocean right now and I’ll be using one of test domains that I own. strapi.guru