we don't know, next game isn't out yet, we don't even know who the canon victor of the conflict will be..
and no, a new dragonborn will not be crowned emperor, the covenant that was the entire reason for dragonborn emperors has been replaced thanks to Martins sacrifice, and the hero of skyrim is "The Last Dragonborn" for a reason, they no longer serve a purpose..
and it certainly won't take place in Akavir, not while we still have half of Tamriel unvisited
I do not think that we selected is cannon, our result could easy be wiped out by later action, this is mostly true about ESO too. An high turnover of emperors only a few names is known now, most people had more important stuff to do.
I think the Emperor will die sometime after the events of Skyrim but before the events of the next game. This way, they can word it loosely so that it can be interpreted that those who choose to assassinate the Emperor will be the one responsible for the Emperor's death and those who didn't do it, the Emperor will die of illness or natural cause.
They can easily say multiple attempts at assassination were made on the Emperor's life and eventually, the Dark Brotherhood who was at one point believed to have been completely wiped out by the Empire succeeded in killing the Emperor causing the Empire to fall into Chaos. Seeing a weakness in the Empire, the Thalmor... etc...etc...
There you have it. If you have sided with the Empire and destroyed the Dark Brotherhood, it turns out there were still survivors who succeeded. If you side with Dark Brotherhood, then you will be the one responsible.