I am still hung up on one point of the OP. Every point on the plane is visible but is there a way to distinguish distance? If so, then I still contend that it would appear to be a bowl shaped like half a sine curve of infinite wavelength. If not, then I agree with Colophon’s mathematics HOWEVER, we also need to take into account the brain’s perception mechanism of “the ground starts out below me but it rises to eye level”. Would the brain interpret the plane as a bowl similar to how lack of depth perception causes the brain to misinterpret this scene?
Again, it would look just like the real world, since the Earth is large enough that it’s very close to flat. Does Kansas look like a bowl?
If I’m standing on a plain in Kansas, does the horizon appear to me to be at eye level?
In fact, the grouns appearing flat is an opical illlusion because it actually curves away from you.