Is there not internet bandwidth involved? Bandwidth for one person means less bandwidth for another, doesn’t it?

Internet bandwidth in America and Ukraine are completely separate. Starlink is mostly bent-pipe, sending signals to station in view of the satellite. Over remote areas, the satellites need to talk to each other to relay signals. But my understanding is that goes to the closest ground station.

How Starlink works: https://www.youtube.com/watch?v=qs2QcycggWU

Its nearest ground station bounced off nearest satellite, or some inter-satellite laser links to make some hops, then to the user. It's optimized to be shortest route, just like routers with the wired internet you're using now: if you stream a movie, that request goes to in a short path from the server to you. You streaming doesn't slow down someone in China, because the data never approaches any equipment in China. Same with Starlink. Their data never approaches any starlink satellites in the US. When they get the whole grid laser link working, then it might, but it will still approach being optimal, with ground stations used as needed.

Ground vs laser is a latency thing, more than a bandwidth thing. No need to stream Netflix with low latency.

There are what 150 gateways/ground stations. That’s a finite number, no?

a ground station in the US can't see a satellite over Ukraine

Precisely. You need to build ground stations near your users.