It's not about blocking the sky. Starlink sends the internet connection back down to the ground somewhere in the country you are in.

That being said, if I have an American starlink account, and I go to Indonesia, what happens? Does my internet connection go back down through Indonesia or does it go through somewhere else?

Starlink is a legitimate business (ISP) that wants to make money from customers in that country. They will comply with all of the regulations and bans imposed by the government in that country or risk getting banned completely.