Kind of a left-field pic, and def not exclusively for running docker, but TrueNAS Scale offers a nice abstraction for running docker containers, with the simple webui interface you're asking for. I believe it uses K8s under the hood, and it's coupled with NAS software, but this seems maybe the closest to what you're asking for that I've seen.
I was going to suggest this, too. TrueNAS Scale is the quickest and most "it just works" version of bare metal --> docker containers with a web-based UI that I have experienced.
