but then how would in game lore handle it afterwards? How do you determine, story-wise, who won?
You dont thats the major issue here, thats why we always fight against a third faction in a 2 faction mmo.
You cant make a playable faction win something like this.
but the senate would be killed or taken as POWs.
You know the republic is fully based out the Senate? Its like killing the whole Moff and Dark Council, it would pretty much fall into complete anarchy.
The empire currently doesnt have the manpower to take over Coruscant anyway. (See False Emperor and the Explosive conflict/ Terror from Beyond story line.)