A part of me suspect the mention of relearning Heavensward may mean the next expansion may go to Sharlayan and we must reason with them to open up their gates and change their old ways like we did to Ishgard. The War we end this time is the long time war against Garlean Empire as that has been our Dragonsong War since the beginning of FF14 storyline.

Though that is only one of the things I suspect why the developers want us to remember Heavensward as something important for the upcoming storyline.