Aside, but maybe important: note that for free accounts Docker Desktop no longer allows one to skip updates. So, installing Desktop before shipping the Windows machine is not going to give the user a maintenance free experience.
As for Docker EE Windows, indeed no longer supported by Docker Inc and meanwhile rebranded to Mirantis Container Runtime: in December 2020 I’ve been told by Mirantis that this only runs Windows containers. If that is true and suffices, then maybe you can automate installation.