How to explain an unofficial research sabbatical on my CV?
Given that it sounds like the university was aware of your plans to come back and seems to have kept your original faculty position for you while you were on sabbatical, you don't have to list this as separate employment. Sabbaticals are well understood within the academic field; listing it separately is just confusing things.

You may want to put the sabbatical as a sub-bullet under your academic position on your resume just to emphasize that (1) you're a cool enough person that your university allowed you to take sabbatical (and held your position for you until you came back), and (2) you have experience doing research outside the university setting.