I have thought a little about how networking and communication works in the honorverse. While something like the internet is very usable on one planet, the current protocols break down even for intra-system communication, much less for FTL travel.
It's not clear how far computing performance has come in roughly two millenia. Past progress was exponential, but we are already hitting problems. Nonetheless, in the Honorverse you could probably fit a 21st century data center into a pack of cigarettes, both in terms of datastorage and computing. If you really wanted to. Many consumer devices would exchange the computing power they don't need for cheaper manufacturing and longer battery life.
The "internet" landscape of the honorverse hasn't been filled with any details yet. We don't know what kind of Twitter and Facebook clones they might use. I could guess that something similar to Youtube would be a very ideal distribution for holo media across space and time.
But how would average people send E-Mails to other planets? How would they watch a video from the other end of civilized space?
My guess is they have something I would call the Ripple Net. When someone wants to broadcast or transmit a chunk of data, he stores it in the local ripple stream. This stream contains packets of data, with origin and (optionally) destination and meta data. Obviously the data is often encrypted beyond belief. The stream is stored in a space station orbiting a planet, for example.
When freighters or dispatch boats "touch base" they synchronize their copy of the stream with the local hub. Because data density is so high, dispatch boats can probably store years of this stream from the entire galaxy. Cargo ships certainly can, without breaking a sweat.
So these ships carry the packets to their next port of call, and over time, date ripples out from one corner of the galaxy to all other corners.
When a user (most often it would be a local provider though) wants to query the ripple net, he asks the local hub for packets for his query, and decrypts them if possible or necessary.
A Youtube clone for example would accept video at a local data center, store it together with other videos, encrypted, of course, to local stream hubs. The packet ripples out, and at each system there is a local data center decrypting the video and offering it to their local users.
This system would work for public and moderately private data transmission. More explicit or secure routing, with higher guarantees of distribution might be available at a higher price. The Peeps didn't use such a system at all because they didn't want uncontrolled inter-system communication.
Who pays for it? Probably just with the current internet, it can get complicated. Many star nations would have an interest in maintaining the infrastructure and even running dispatch boats on important routes. Many corporations would, also. But due to the high data density it just doesn't matter in terms of cost if you carry only some data or "all of the data".
Many limitations mentioned in the books don't support this theory though. For example data chips that are used like floppy disks (HH1 was written in the 90ies) seem to be used extensively. The specifics of the correspondence between Old Earth and Manticore regarding the Talbott incidents for example preclude a RippleNet based on dispatch boats.
The Sollies wouldn't have had to wait for a message through the junction or by the direct route, because someone on Spindle would have blogged about it...