Little gaps between visas don’t break the 7 years. Also, IANG Visa can only be extended if you can prove a work contract I think. So if your current IANG visa does not last the entire duration of your studies you might need to switch to a student visa anyway.
also, I wonder if you can just apply for your IANG visa again once you’ve graduated from your new degree.
Good question from your side... quite many mainlanders do masters right after bachelors, but I am not sure if they use new study visa or IANG.