As I am teaching myself right now maintainable selfhost setups using popular apps (admittedly with Kubernetes vs something minimal in functionality like Docker Desktop), there is a lot of complexity involved in getting these services both functional and maintainable while also having to consider the security implications of various setups.
While I agree the concept of self-host is a good thing to advocate, I think the complexity and difficulty involved not just to do it, but to do it right is going to be a straight cliff of a learning curve for those not already technically inclined in databases, networking, and filesystems/block storage.
Honestly, taking the burden of being IT for a reasonable subscription cost for your efforts is a better way to go, especially if the setup allows for expanding your offerings to other members in a localized community.
The flatpak documentation has a semi-relevant page on setting up a flatpak repo utilizing gitlab pages and gitlab’s CI runners on a pipeline. Obviously, you’d need to substitute Gitlab Pages for a webserver of your choice and to port the CI logic over to Gitea Actions (ensuring your Gitea instance is setup for it).
A flatpak repo itself is little more than a web server with a related GPG key for checking the signatures of assembled packages. The docs recommend setting up the CI pipeline to run less on-commit to the package repos and more on the lines of checking for available updates on interval, though I imagine other scenarios in a fully-controlled environment such as a selfhosted one might offer some flexibility.