What CLI commands do I need to use in order to check if the image in my private docker registry is a newer version than the one currently running on my server?
E.g.
Not sure about the version but if you mean the tag of image, it can be easily checked through the registry v2 api . Note that in context of docker images tag has nothing to do with the version of software.
Use curl command in CLI
curl :/v2//tags/list
To get a list of repositories pushed on the private registry, use
curl :/v2/_catalog