How about a huge collection of offline digital medias and an Intranet that connects the sailors on the ship? That might help a bit?
Your average techie can get around that by using Jellyfin, Sonarr/Radarr, Torrent trackers and such, but the military has to follow the law.
THe fact that ships travel around the world doesn't make this easier. Even if the Pentagon could make a deal with most of the major U.S. streaming services to provide their content to the military in a secure, offline fashion, which they probably could, those companies are often prohibited from distributing that content outside U.S. borders due to exclusivity agreements.
The US Navy could have their own version of that.
I recently flew on long flight with Qatar Airways and their library is massive. Almost any movie, show or album I could think of was in there
Purchased (i.e. not rented) media on at least iTunes/Apple TV/Apple Music/Kindle etc. are usable offline indefinitely.