How should I ask a potential advisor why they haven't published in the last 3 years? I'm using a throwaway account for privacy. I know professors are human beings and "I can just ask", but, as this is the start of the relationship, I don't want to seem rude - or to seem that I am interviewing them. This potential advisor has published papers in top journals before, but nothing for the last 3 years.

I know this question is related: PhD with a supervisor who has not published anymore since 2014, but this professor is quite young, so the situation is different.

I think that if I ask them about "their current research interests" they will just talk about the current project that is about to begin - without addressing the issue I'm interested in.
Instead of a question that might be insulting, you should probably ask them what they've been working on for the past few years. You need to know that in any case and their answer might give you the reason that they haven't got anything out recently. There may be a lot of work in progress but not yet ready. That sort of thing can actually be an advantage to you and knowing what it is, certainly is. 

But if their answer indicates not much research, then you might want to keep looking. 

By the way, this is a topic for a sit down conversation, not just an email. The latter might work, but would require more work from the prof and so you might not get as complete an answer.