Here's what I've come up with so far.

What works*

Presumably most CLI commands would work, to whatever extent the Podman CLI has parity, but I haven't looked that far into it
Containers list along with at least most related commands
Images list along with at least most related commands
Prune actions

*Had to connect with Remote - SSH since there's no clear way to reach Podman remotely, more on that below

What does not work

Debugging could only possibly work for Linux users as it is heavily dependent on the daemon being local
Quite a few properties from the Docker Engine API are missing in containers, images, and networks listing. For example, the Created/CreatedAt values are inconsistent; no container status; no network ID.
Creating networks
Anything pertaining to volumes (404)
Anything pertaining to contexts
Containers list won't show stopped containers
The API service has to be manually started each reboot which is annoying (though it could definitely be configured to start automatically)
- It is also per-user, consequently it cannot use constant socket paths
docker-modem would need to be changed to support Podman over ssh, since it uses docker system dial-stdio which would not work
No current documentation on setting up an SSH connection with the remote client (all that I could find pertains to the legacy varlink implementation)
There is either no API documentation or I cannot find it. The Docker engine API documentation is not a good substitute as there are too many inconsistencies. At a minimum, these inconsistencies would need to be documented.

@Nuc1eoN, @JacekPliszka, anyone else -- what are your primary use cases? How serious are these limitations for your workflows?