Ok I think I got it.
The world they're in right now is some sort of shared consciousness or simply, dreaming. The idea came to me when Chii woke up in the theater in the movie chapter of the anthology.
But this is where it gets better. The sister might actually be trying to save the world. In the last moments of GLT, we can see that humanity escaped the planet on a spaceship. The rest of humanity must be in cryosleep for the long journey. Everyone is sleeping and sharing a dream world which is this Shimeji Simulation, maintained by the AI of the ship (god/little girl). The apartment blocks represent the countless cryosleep pods and then here is the problem, several rooms are now empty. The people in these pods may have woken up, died or something else. MC's sister is trying to get out of the simulation and check the situation in the ship and fix the problem.
Now, why is Chii and Yuu in this universe. In the last moments of GLT, the pair reached the highest location of the country, which may have been the control tower for the spaceship launch, given the details that were presented in that chapter. The system for shared dreams aka Shimeji simulation must still be active in that location and when both of them slept, although their body died, their subconscious joined the simulation.
The good ending would probably be that humanity has arrived in a new planet, the ship is sinking and swimming with the fishes but sis saves the day by waking up everybody and getting out of the simulation while also saving the simulation world for Chii and Yuu and other people that died in the journey.
Bad ending is that, this is the ship that failed to escape the planet hence the signal is closer and Chii and Yuu joined the server where everybody is actually dead ( I hope not).
This and Vertical country are really good mind trip manga, I ahvent solved vertical country yet but I hope i got this right