Do a few experiments and you will see what I mean.
You have suggested experiments a few times. Here is one you can do. Telescopes are very powerful things. With the Hubble Space Telescope, for example, we can see details of galaxies 100 million light years away. With a good strong backyard telescope we can easily see the craters and mountains of the moon, and we can easily see the rings of Saturn and the Moons of Jupiter and the Great Red Spot. We can easily see all of these things hundreds of thousands or millions of miles away in great detail.
So, get yourself a good strong optical telescope and go look at the Moon, the Rings, the Great Red Spot.
Go show yourself directly how well that you can see things at tremendous distances.
Now go up on the roof of your house and look around your range of vision, as far as you can see in any direction along the land until your vision is blocked by a tree, a hill, a mountain, a building. Now peer through your telescope at that farthest object. The farthest I can see from my house, other than looking straight up, is less than a quarter of a mile, because I live in tree-tangled Connecticut, where everything is beneath the trees and the sky is only visible above the trees, about 45 degrees off the ground. I can see the trunks and the big boughs of those trees a quarter mile away. I cannot distinguish the individual leaves. But if I pointed my strong telescope at them, I could make out the leaves and the birds easily.
You do the same, to demonstrate that at short distances you can see everything pretty plainly with your telescope.
Now take a vacation. Go out West, to the Grand Canyon. Go up on a rocky promontory and look over at the other rim, a mile or more away. Now look up the Canyon at the crack and it winds off to the North and East or South and West. The air is clear, the desert is mostly flat. From your little elevation, you can see many, many miles, to the mountains and mesas in the distance. Now point your telescope at those things in the distance: they are sharp and clear. You can make out the boulders. You can see that which is 15 miles away. If you go up a mountain, you can see that which is 25 or 30 miles away. With the telescope, in clear air, you can see everything in the range of vision clearly with your telescope. Nothing is faded or fuzzy. You have only a small sight picture through the tube, but what you see, you see clearly.
From the mountain top you can look through your telescope and see very clearly the houses that are 25 miles away. You can see their windowframes and lightbulbs at dusk.
Now come back down the mountain to the foot and look down down the same sightline. You cannot see the house, or its lights, even through your telescope. What you see is some piece of ground between here and there. If you had the Hubble Space Telescope, you could not see the house - because it is blocked by the earth.
That is the effect of the curvature of the earth. But, of course, as we have said before, the hard ground doesn't conform to the shape of the earth. Mountains rise up, uplands are thrust up. That blockage may not be the curvature of the earth at all, it may just be the result of seismic activity moving pieces of the earth's crust around.
Now take your telescope and go to the ocean beside a seaport on a sunny and clear day. Set yourself up next to a lifeguard tower that is unoccupied. Pick a ship leaving port and focus your telescope on the name on the stern, the letters and the sternlight and the flag that it bears. As it nears the horizon, watch it intently through your telescope. You can still read the letters and see the flag. They do not disappear into the haze. But you see it all getting lower and lower in the water, and you see the individual waves moving up next to it and past it. And then you can't see the letters any more, because the ship has followed the curve of the earth and that part has dipped below the horizon. You can still see the stack and the upper superstructure, but not the name or the colors on the stern.
Now go climb the lifeguard station with your telescope and point it right at the stern. Presto - you can see the name and the flag again, perfectly clearly. Keep watching, and they will sink below the waves again.
It is not a matter of visual acuity failing or the ship no longer being visible through the air. As you noted, you can still see it clearly with a telescope. But then you can't - because it went below the horizon because of the earth's curvature. If you had the Hubble Space Telescope and the earth was flat, you could see the coast of France from Cape Cod. You can't. That's because the earth is round.
You can conduct this experiment yourself, with telescope or binoculars, as many hundreds of times as you like, and you will always see the same thing.
I HAVE conducted that very experiment, as part of my work at sea, watching ships rise from over the horizon until I could identify them and their heading, and watching them sink back over the horizon steaming away. In the middle of the ocean on a four hour watch there is not a great deal to do, so another ship is a thing to look at it, so you do, and you see just exactly what I have described, over and over again.
These are practical, real world experiments you can do to satisfy yourself that yes, the world is in fact round, and no, the atmosphere does not so devour light that you can't see past 10 miles or so. That's certainly not true. You can see stars trillions of miles away, and you can see a light on a ship as far as you have a line of sight to it. If you go up in a helicopter, the distance to the horizon extends and you can see farther. If it is clear, and there is a light, you can always see the light.
It is true that at the horizon, the atmosphere seems to refract the light and make things bigger. You're looking through a lot more air molecules that lens it when something is right at the horizon than when something is above.
You've seen the big rising sun get small, the big rising moon get small as they rise off the horizon, and the sun get bigger and bigger until its finally huge as it sinks into the sea. We have all seen this. Some have asserted that it's an optical illusion. That is not true. You can measure the arclengths of the horizon that the sun or moon takes up as it settles into the water, and compare it to the arclengths when it is high in the sky. The setting sun doesn't just LOOK bigger, it IS bigger, MUCH bigger.
Again, these are simple tests you can do yourself to satisfy your mind, if you really want to.