https://i.imgur.com/StrKpH0.jpg
Image source: https://www.bookharbour.com/freiberger-yacht-sextant
Who is saying that the sextant doesn't measure the sun? It can even measure other stars that are much farther away. But because of its limitations, the sextant can't tell how far they are away, or how far the sun is away. This doesn't mean that the sextant doesn't measure the sun.
But it DOES mean that you don't measure straight up at 90 degrees. Rather, you measure straight up at zero degrees. When measuring an overhead sun, 90 degrees shows you a position slightly above the horizon.
Your calc that tells us how you think a sextant measure the sun is incomplete and incorrect. All the sextant tells us is the angle. If the sun were 93 million light years away, and were the corresponding diameter (a light year to a mile), it would appear almost the same as it does.
You are sadly mixed up, or criminally trolling.