The curvature you see is caused by a fisheye lens. This is well known. But there are many videos available where fisheye lens' were not used, and everyone of them shows a flat horizon in all directions. With the horizon always coming up to eye level. Research it. Literally anyone can send one up now to see for themselves with a GoPro for fairly cheap. Kits can be bought online for $500-$1000. And they will get you up into the stratosphere at over 100,000 ft. I got one, and I'm sending it up August 21 to view the eclipse from an area of totality. I will post my footage.
No it doesn't.
Only when they are close to the ground or with a small FOV does it show a "flat" horizon.
The other times it shows a flat horizon is when the horizon is below the centre of the FOV of the camera, resulting in the fish eye lens distortion distorting the curve into a straight line, or when it has been passed through a filter to "correct" the fish eye lens distortion by making the horizon straight.
The horizon is always a circle, centred on you. It is technically flat, as it can be described as the intersection of a plane with a sphere.
But in no case has the horizon been at eye level.
The only time that happens is when your eye level is ground level.
Pretty much no footage in the world can easily show that, as you need to know the orientation of the camera.
The easiest way to do it is with a few wide angle cameras all strapped together and aligned, and their footage stitched together into a panorama. (which you can just use a 360 degree camera for).
If the cameras are level, then the horizon will be a line all around the FOV (thus a circle). If it is at eye level, it will be vertically centred. If it is below eye level, it will be below centre, if it is above eye level it will be above centre.
If the cameras are not level, then the horizon will be a circle which will appear as a wavy line. The section where it is highest in the vertical direction of the picture will be on the camera (or part thereof) pointing down the most, and the section where it appears the lowest will be on the camera pointing up.
These will be 180 degrees apart.
If the horizon is at eye level, then at 90 degrees from either location (in either direction), the horizon will cross the vertical centre of the camera and the extremes (the highest and lowest vertical position) will be the same.
If it is below eye level, the extremes will be lower than expected, with the higher location not being as far above the centre of view as the lowest location is below it.
It will also cross the centre of the FOV closer to the high extreme, rather than midway between the high and low.
Unless it is so far below that high extreme doesn't' even go above centre.
(It being above works the same but in the opposite direction, so every point moves up, so it crosses closer to the low extreme or the low extreme might be above.
You can test all this by getting a ring and seeing how the cameras acts at various angles with the ring at the same height as the camera (eye level), above it or below it.
Also, the vast majority (if not all) of the go-pro family have wide angle lenses which will result in significant distortion.