If the star can be seen from both the US and China, and it is half way between the two
What if it's NOT halfway between the two? That's my question.
And when we are talking about celestial navigation it is more about what it looks like then actual distances. The person does not need to know exactly how far the star is to make the navigation work.

The distance of the star, determines where it is in relation to the horizon, as you describe below.
"A star chart functions in navigation by providing a visual map of the night sky, allowing navigators to identify specific stars and measure their position relative to the horizon,
The north star, for example, doesn't move. So this star will be in DIFFERENT positions on the horizon (using a globe model), if you're in the US vs China (i.e. china can't see the north star). But if the earth were a spinning globe, everyone should be able to see the north star, at some point during the day, because a) the north star doesn't move and b) the spinning earth would be a like a clock which would round every number, at some point during the day.
A FE model will show the north star in the exact, same spot on the horizon, no matter where you are in the world. Because everyone is looking up. That's why china can't see the north star. Because the earth doesn't move.
This is why most calculations are done as if the earth is flat because it is just easier to do the calculation.
No, it's because the globe calcs don't make sense.