Indeed it seems the dragon in the Heavensward logo is truly Midgardsormr after all.

He is not a primal though as he left a corpse when he died whilst primals merely return to aether. He is a mortal dragon, though it seems he can and will be resurrected somehow. I would imagine he has an echo to share with us before he returns to rampage against Ishgard (based on what Iceheart told us).