You are over thinking. Just tell them that you were studying. As long as you have the physical present days and have proof that you studied in Canada, you are fine.
Canada doesn't force their PRs to work in order to get citizenship. Or care that you studied somewhere else before you settled in Canada.
btw. I hope you have filed tax event without income, it's good for you. (likely get credit on things like GST etc)
again it's not a must do for citizenship. But if you did file tax, your NOA is another piece of proof that you can provide