I have a question about why the HOME directory is not being set/used in the way I expect within the Dockerfile. Would this be on topic for ServerFault (because the question is about Docker, and hence "server administration" in that loosest sense), or is it more suitable for Stack Overflow?
I can't tell you if it's more suitable for SO or not, but the question you describe sounds like it would be topical on Server Fault, yes.
I think anything that is related to operating servers and server technologies belong to Server Fault, even if it seems like it's programming. System Administrators should do some programming - programming to automate, to deploy, manage, etc. This question would be useful and more appropriate than many of the questions that get posted on SF every day!
I would think that configuring Docker for an app would be a stackoverflow question, administering docker containers (Kubernetes) would be an admin question.