I believe it's not the entire library, bus a dynamically maintained cache of the most popular content over that connection.
More seriously, the problem is a static dump will get old very quickly, and keeping the internet "up-to-date" will require an enormous bandwidth to the spaceship.
> According to Netflix's own documentation, "An individual appliance can offload approximately 60%-80% of content requests depending on country catalog size," but when units start working in pairs, the storage size can exceed the size of Netflix's library for a region. And when this happens, the pair will use their excess storage to double up on stuff to help deal with high demand, or to make sure that if one fails, the other still has as much content as possible.
> More seriously, the problem is a static dump will get old very quickly, and keeping the internet "up-to-date" will require an enormous bandwidth to the spaceship.
No need to have the entire internet, just the most popular tenth of a percent, and just daily updates of what's new. https://eyes.nasa.gov/dsn/dsn.html is currently downloading from Mars at 3 megabit. I'd expect Earth-to-Mars can be much faster than Mars-to-Earth from a car-sized orbiter with a small dish and limited power.
For Netflix, just send a new box every 3-6 months on the next rocket. The ISS already gets in-theater movies well before they're released on DVD, so you could even have release dates synchronized for no delay whatsoever!
More seriously, the problem is a static dump will get old very quickly, and keeping the internet "up-to-date" will require an enormous bandwidth to the spaceship.