The Docker license is for Docker Hub features and in case of large companies, for using Docker Desktop. You can log in on as many machines as you want. Pulling images from private registries or repositories on Docker Hub don’t require any subscription, so if you want to share your images and you have a client for which you develop an application, and the client runs Docker CE and not Docker Desktop (which is only fo development), they can just use their own account for free.
Of course, if they want to run Docker Desktop, and the client company is a large company, they need their own subscription.
I guess, you could use your account on their Docker Desktop just to download the private images and then log out, but the subscription is for a person, you couldn’t share your account with your subscription if that is reqiored fo the application or if they want to use your image for development on Docker Desktop.
Note that although I’m pretty sure it works as I interpreted it, I’m not a Docker staff member and I can’t legally allow you to do anything. So if you are not sure that you are doing something legal, you could try to contact Docker support or maybe write an email to legal@docker.com
I recommended this email address a few times, but I don’t know who is reading it and how frequently.