I have never used Podman Compose but it exists. I guess it's really similar to docker compose.
With podman you can use "Quadlets", which are systemd files allowing the services to integrate very well with the system (you can use journalctl to see the logs of a container).
Podman supports building, and starting containers (and creating vol‐
umes) via systemd by using a systemd generator. These files are read
during boot (and when systemctl daemon-reload is run) and generate cor‐
responding regular systemd service unit files. Both system and user
systemd units are supported. All options and tables available in stan‐
dard systemd unit files are supported. For example, options defined in
the [Service] table and [Install] tables pass directly to systemd and
are handled by it. See systemd.unit(5) man page for more information.
The Podman generator reads the search paths above and reads files with
the extensions .container .volume, .network, .build, .pod and .kube,
and for each file generates a similarly named .service file.
Yeah, they are losing an easy access to a lot of players.