The purpose of quadlets is when you want good integration with systemd.

The better equivalent of docker compose is podman kube, which does use a single file. And it isn't bespoke, it uses the same format as kunernetes.

And if you prefer the docker compose format, podman-compose is available as a separate tool.

And FWIW docker compose is a separate tool from docker itself as well (and needs to be installed separately on several linux distros). And can actually work with podman instead of docker.