A new not-what-I-was-looking-for-but-it-works-solution:
I'm mirroring the Dockerfile/project from my local Gitea to Gitlab.
I've set up Gitlab as my registry for the project.
(The project in this case is a Grocy package for Cloudron.)
This arguably gives me a private-enough repo for what I'm exploring, but I was hoping to be able to entirely leverage my Cloudron for this.
I'm just plain confused why, at some point in the past, my locally-hosted registry worked, and now, it does not. This is why I believe there is "crufty" config laying around, somewhere, and things therefore don't work.
(But... this makes almost no sense, because I have uninstalled and reinstalled the registry, so it is not clear how any state could persist.)
Anyway. This remains a mystery, and I would need some explicit guidance as to where I should dig around in the backend of Cloudron to figure out why things are not behaving. (It could also be that there's still some port that I don't have open, or... 🤷)