just stop those test containers with the docker stop command instead of using docker-compose.
docker-compose shines when it comes to start together many containers, but using docker-compose to start containers does not prevent you from using the docker command to do whatever you need to do with individual containers.
docker stop project_nginx_run_1 project_web_run_1
Also, since you are debugging containers, I suggest to use docker-compose exec <service id> bash to get a shell in a running container. This has the advantage of not starting a new container.