A huge distance is actually a helping factor in this case. A 1.75 meter person can see 4,700 away before the horizon curves out of view. That means (ignoring the bending of light by the atmosphere still) the viewing angle allows for 1 meter "down" every ~2,685.7 meters out. The radius of the Earth is ~6,371,000 meters so to be able to see the middle of an object from ~the radius of the earth "down" with that viewing angle would require the object to be a minimum of ~2,685.7 * 6,371,000 = 17,110,594,700 meters away. That's a minimum distance of ~0.11 AU so the person would only get a partial view of the moon but a full view of the sun because the moon -isn't- far enough away! Well technically the Earth could rotate slightly farther while having the middle of the sun still visible but I'm too lazy to calculate if it's actually enough, my hunch is no. If you wanted to see the middle of the moon and the middle of the sun (with no bending by the atmosphere) during an eclipse you'd have to be near the top of Everest while it happens to be exactly rotated between each.
Forgive the hasty diagram but https://imgur.com/a/aoZIZTs
The Earth is entirely in-between the wildly out of scale Sun and the Moon, but a giant standing on the "top" of the Earth can see both.
I’d also question if this can have any meaningful effect on the sun, which is about 23500 Earth radii away. That’s a very, very slight perspective shift.