This is one of those things that I've always been too scared to ask so I'm just going to ask it now: Is there a distro designed exclusively for running docker (and perhaps other) containers that also contains a friendly web UI for people who have no idea how docker actually works?

I'm familiar with Proxmox, but it doesn't natively support docker.

docker-the-company maintained https://github.com/linuxkit/linuxkit when I worked there. I have no idea who maintains it now, but it looks like it is still active (presumably still docker-the-company, since their adopters list [1] lists docker desktop).

[1]: https://github.com/linuxkit/linuxkit/blob/master/ADOPTERS.md