Why not just write something (or use a pre-existing tool) to update your docker containers? I know on Kubernetes there's plenty of tooling around Helm.
I redid my docker stuff with podman and quadlet recently and it's been great. Quadlet turns the containers into behaving like regular systemd services (i.e. you can trigger them with timers), and "auto update" is just setting Pull=true when the container re-runs (there's a heck of a lot of good reasons to also not do this).