I think it's very likely we'll see Atrithau early(ish?) in TNG, for all the reasons you pointed out. Things over there
do seem to have been in quite a bit of disarray even before the start of the Second Apocalypse...it's likely whatever they manage to accomplish there won't last for long.
I have a guess which may be entirely wishful thinking - they might go to Conriya at some point (geography-wise people, feel free to tell me if I'm being a complete idiot here). Esmenet has already been established as trusting Proyas' wife (now widow) Miramis, and actually thought of finding refuge there following Maithanet's coup:
She understood the force of his argument--not a day passed where she failed to inventory all those she thought she could trust. House Nersei, in particular, in Aöknyssus. Surely she could depend on Queen Miramis--Saubon's niece and Proyas's wife--to at least give her sanctuary, if not prosecute the interests of her family.
Of course,
Miramis might not be so willing to help out the widow of the man who set up her husband to be executed as a traitor (especially if they only go there after months have passed and
Mirathais and other possible survivors have had time to take news back to Miramis). We don't know what Miramis' relationship with Proyas was like (considering he wasn't even around most of the time), but I'd be very surprised if there weren't at least quite a few people in Conriya who refused to believe or at least were strongly suspicious of the accusations against Proyas. He seems to have been a well-loved king.
On Zeüm - I think Akka and co. may not go there for quite a while, but we'll get an idea of what is going on there before that via one or more new POVs (Likaro, another Mbimayu sorcerer, maybe even the Satakhan or any of his surviving family members before they get murdered by the Malowebi-faced demon...).