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.
The potential common cause points toward the GPU drivers (note of games in Proton, libgtk4 segfaults, and libnvidia-glcore segfaults). What nvidia driver version is in use. A quick search found a rough match to shown symptoms, but is recent and matches the hardware (NVidia Polaris desktop). Perhaps the driver version in use exhibits a similar showing of a regression for such GPUs?