Flat Planet Mode, now known as the Conspiracy Pack was added in update 5.1 on 20-07-2019. It could be purchased for $7.99 and is not included in the all-access pass. It allows the player to view their planet as if it was flat, and added some new events. The planet still spins on a (relative to the screen) vertical axis. One side of the planet is completely lit up, while the other is completely in darkness. City lights can still be seen on the dark side.
You can toggle flat planet mode on and off at any time on the full planet view screen. This will toggle all of your worlds at the same time. See 1:26 on the tutorial for flat planets.