Best practices for Docker compose testing?

In complex orchestrations of docker-compose.yaml stacks, I'm keen to do a simple integration test that shows the system works. I'm not entirely sure though this might be called an "end to end" test.

I've seen https://github.com/bats-core/bats-core used in helm charts, though not so much in docker-compose.yml.

Is there some other testing method that I am missing? Or is using bats in a docker-compose context, a reasonable approach? My end goal is that the application can be testing in some CI service like TravisCI/CircleCI using a simple docker-compose.yml & a command not too dissimilar to docker-compose up