Summoning @nyrath
This is an idea I've definitely been toying with lately to prepare for my sci-fi GURPS game, though even in that setting, people have FTL ships, just not FTL radios, so they end up dropping off big packets of data that might be of value to a general audience like the news and there's a flourishing letter-writing culture.
I suspect it would be much more like the old web, where you would use a relatively low-bandwidth format like text to browse for big high-bandwidth transfers.
But at a certain point, like interstellar distances with no FTL, surely the idea of having a network would just break down and it'd be more like isolated libraries and you might see policies like Alexandria supposedly had, like "give us a copy of all your data so we can keep and distribute it, and if you refuse, we refuse docking permissions."
@chakatfirepaw @squeakyears @maxissakitsune @nyrath
Those too young to have used it might want to look up uucp.
Or FidoNet.