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.
I know ArchLinuxArm (a fork of the ArchLinux project) supports the Hisense C11. It does seem to be a fairly involved procesd, and (potentially?) requires using external media rather than the onboard eMMC storage to boot a Linux system.
Your particular Chromebook contains the same SoC (Rockchip RK3288) as an Asus C201, which Debian has an install guide for. Once again, a fairly involved process and this one may not be guaranteed to work if the C11 has some quirks not present in the C201.