Every container system is "docker-like". Some (like Podman) even have a drop-in replacement for the Docker CLI. Ultimately there are always subtle differences which make swapping between Docker <> Podman <> LXC or whatever else impossible without introducing messy bugs in your workflow, so you need to pick one and stick to it.

If you've not tried it recently, I suggest give the latest version of podman another shot. I'm currently using it over docker and a lot of the compatibility problems are gone. They've put in massive efforts into compatibility including docker compose support.

Yeah, from a quick glance the options are 1:1 mapped so an

  alias docker='container'

Should work, at least for basic and common operations