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.

Podman is good, you should try it.

Most docker’s commands can be replaced by podman’s.