Any idea on how to make a world loop seamlessly like if it were a sphere but on a plane?
Odin sphere for ps2 does this.
What I would do is to use triggers which would read whether the player has reached a certain point and, if they have, instantiate another copy of the plane in the appropriate position.
So, if the player enters the northern trigger, the game would load the plane in the position appropriate so that the player could just keep walking in a northern direction and reach the newly-loaded plane.
You could use a similar system to unload previous planes (which you would need to do for the sake of resources and footprint).
These two tutorials show you exactly what you need to know to achieve this.
I personally would create the scene as a cylinder (with the sides facing to the inside), and instead of moving the player, I would rotate the environment. (Alternative: a flat circle instead of a cylinder)