Publishing an action that just uses a container (but doesn't build it)

I’m looking to publish an action to the marketplace that will execute using a docker run, rather than a full build. Is there any way to do this?

Also, what’s the best way for pausing the docker container while running so that I can debug it?

I believe by default the runner will build the container, if that is what you mean by this question. That is, with the examples from the docs.
To work around this you can build the image and publish it to e.g. Docker Hub. You can see an example of how to use a image from Docker Hub for a run here.

When develop and publish a Docker container action to the GitHub Marketplace, you do not need to build the image. Because when using the Docker container action in a workflow run, GitHub will download the source code of from the action’s repository and automatically build the Docker container.

We seems have no methods to pause the Docker container for debug while running in the workflow, but you can try enabling debug logging to get more debug logs.