In Docker Compose v2 they had a more sophisticated "depends on" model with health checks, but they removed it in v3. The docs say something about Docker Swarm so I'm guessing they removed that in order to try to make v3 syntax work for clusters too.
The real tragedy here is that Kubernetes won, but we're still stuck with Docker Compose trying to be the same thing.
I hope your tool can help change this annoying status quo!