I don’t recall a dispute over royal titles before and how they would apply to commonwealth nations. For the most part in Canada there are minor trappings of royalty. Mostly representatives of the monarch in Governor Generals and Lt. governors to sign legislation and open parliaments. Long ago they were appointed from England but now are locals. Other than that Royal visits are about the extent of it.
It seems Harry living in Canada is a big deal to some as per that newpaper in Canada. They want to maintain independence and not have a Royal living in Canada.