Great-circle curvature is simple math, and simply measured in reality. On a #FlatEarth, nothing would ever be hidden by a sea-level horizon - including (and especially) the Sun. If you ever experience that condition known as "night", congrats, you've debunked #FlatEarthers.
Left-to-right curvature is a good bit more complex mathematically. Your sea-level horizon is a planar circle, the frustum of your view-cone; but it is viewed from out-of-plane 1/
(a hair less than twice as far above the center of the horizon-circle as you are above sea-level) and in rectilinear projection (because that's how your eyes work). If viewed in cylindrical projection, the constant horizon dip would translate into a straight horizon at constant declination. But that's *not* how your eyes work. 2/
In rectilinear projection, this out-of-plane circle - like looking down at the edge of a horizontal hula-hoop centered on your chin - results in a shallow hyperbola with its apex at the center of your view.
This is actually photographable (with considerable difficulty). 3/
That is a custom-built horizontal reference set up 603 feet ASL. When cropped and horizontally compressed, Earth's left-to-right horizon curvature is clearly visible.
(Reference: https://mctoon.net/left-to-right-curve/)
GSV_Empiricist