BarelyYou can keep Docker Desktop installed and run both. They don't share anything: each has its own images, containers and volumes. An image you pulled in Docker Desktop has to be pulled again in barely.
When you open Docker Desktop, it makes itself the current Docker context and can take over /var/run/docker.sock. Settings › Doctor in the app shows which one Docker is using. In the terminal:
barely doctor
To switch back to Barely, switch on Make barely the current Docker context under Settings › Docker. In the terminal:
docker context use barely
To run one command against a specific one, use --context:
docker --context desktop-linux ps
Questions
Do I need to pull my images again?
Yes. An image you pulled in Docker Desktop has to be pulled again in Barely. Each keeps its own images, containers and volumes.
How do I stop Docker Desktop taking over when it starts?
In the app, switch on Set DOCKER_HOST in your shell profile under Settings › Docker. That stops Docker Desktop switching docker away from Barely when it starts.
Something missing or wrong? Tell us.