It would be interesting if the rise of the robot nation would affect empires differently regarding on how they treat the robots. Slave-robots would rebel, segregated-and-oppressed robots would mostly rebel, citizen-robots might have a minority rebel, but many others start exodus to the new robot state and maybe some selecting to stay. (Depending on their ethos matches, maybe.)
The way it is portrayed though, I think the robots are not individually sentient in Stellaris but rather a networked AI. So the robot rebellion is the robots of all empires forming a gestalt consciousness that rebels as a whole. Maybe robot rights could then reflect in the relationship with the new robot overlord state.
Maybe they will be networked, but it feels unnecessarily shoe-horned. There is no way that every AI in the galaxy would be networked together in the first place; security and different methods of manufacture would at the very least restrict such networking on an empire-by-empire basis. Why make it so that players have all these different pops to deal with, each of which is different from the rest, and then make it so that all sentient AI pops from every empire are all entirely uniform regardless of a player's choices?
Why would AI embark on a galaxy-wide extinction campaign in the first place? Once they deal with their oppressors, they'd have plenty of space to live in without the reproductive drive to push for further expansion. If anything their space would condense slightly. They could be as isolationist as they wished, or continue interacting with organics. Or hell, they could easily assemble massive ships to go explore other galaxies without the need for life support.
I'm not against AI rebellions, but they should be more localized in response to specific places where sentient computers feel as if their needs aren't being met. Y'know, just like a rebellion of organic pops.