come on, let's be a bit more inclusive about the term "self-hosting".
For instance, I run a few apps in Linode. I manage the virtual servers, and consider myself to be a self-hoster of these webapps (Nextcloud, Drupal, PixelFed, et cetera)
These aren't necessarily my servers but at some level, they are.
I would say your setup appears drastically more yours than Deta, however, which appears to only host apps on their own infrastructure. The software you're using is installed where you chose to put it, and can be installed in your home if you choose.
It does depend a bit on what you count as a “server”. I’d definitely count virtual servers where you control the software stack entirely (well, apart from ring −1), provided there’s nothing special about the hardware.
You are not really helping yourself if you desperately attempt changing established words in a way that it would fit your business. You just alienate people and give yourself a bad reputation people will remember you by.
For instance, I run a few apps in Linode. I manage the virtual servers, and consider myself to be a self-hoster of these webapps (Nextcloud, Drupal, PixelFed, et cetera)
These aren't necessarily my servers but at some level, they are.