Docker Compose support doesn't see local Docker images

I have a project where I've attempted to do the following:

1. Build an image of the project's application, locally (without pushing into a registry);
2. Set up an integration test suite that runs after the image has been built;
3. Have a test case in that suite that uses TestContainer's Compose support to launch a composition that uses the image from step 1.

This however doesn't work, because TestContainers runs Compose inside a container, and it evidently doesn't see the image that's locally built on step 1.

Another symptom of this same problem is that the Compose container, every time it runs, pulls public images afresh from Docker Hub even though they are locally cached on the Docker host.

The issue names no source files or tests. Start by reproducing the Compose support flow with a locally built image and a cached Docker Hub image, then trace how the Compose container is launched. Done means Compose can use local host images and does not unnecessarily pull images that are already available.