A combination of some of the below (inspired by some answers above)
I'm not sure how exactly your FTL travel works, but if you can produce wormholes for amounts of time long enough to get a spaceship through, you should also be able to use them for data packets, in various ways.
What I don't know is how hard it is to make those wormholes, and whether you can only produce them in certain places, or if you could have a machine in your basement producing small holes of the size of your fingernails, at a rate of one per minute. So depending on how hard this is (or how hard you want it to be), you could combine the methods below in different ways:
For very large amounts of data (and permitting significant latency)
You write the data on some physical storage (flash chip, optical disc, future holographic 3D crystal matrix thing...), open a wormhole and hand/shoot/drop the medium through. It is then caught/received on the other end and read.
Depending on the achievable size/frequency for wormhole creation, and of course the number of communication partners for one node, the process could be highly automated, with several storage media popping into and out of multiple tiny wormholes multiple times per second -- or maybe there's something about those wormholes that makes them a lot harder to create on the surface of a planet, and it requires a huge installation, and regular choices about which request for data transfer should be prioritized.
For smaller amounts of data, and much less latency
These days, wireless communication can be done via lasers (usually not in the visible spectrum, though): Effectively radio waves but coherent and directed, in order to focus the power needed to send and receive for a given signal quality.
With a well-built communications laser/receiver, you would only need a millimeter-sized (or smaller) wormhole to start transmitting. During transmission phase, network speeds could be significantly higher than wired networks on Earth these days (extremely short distance, huge possible signal intensity, using shorter wavelengths than visible light). However, you can't always be transmitting since your wormholes collapse so quickly, and the higher the wormhole creation frequency, the smaller the holes, and the lower the throughput. So realtime communications could be possible, but would achieve fairly low data rates (or be very expensive).
In a scenario where communications are more limited, you might also decide that creating wormholes on planets is pretty unfeasible/expensive, or has other negative consequences (radiation?), and therefore they could only be created in space, possibly at some safe distance to the machine what creates them. In that case, sending data from one planet to another might involve having a small wormhole created by a machine somewhere in orbit, and firing a communications laser through it (probably also mounted to the same machine, which receives requests for data transfers from the planet surface). This would mean no actual real-time communications unless you can pay for one of those machines to make tens of wormholes per second (to the same destination) and guarantee that your data packets will be prioritized.
Moving larger amounts of data via physical media would then also be harder because having some satellite to shoot the storage through wormholes, and catch/process what's coming back is way more involved than having them drop into some receptacle in your basement.
Some poor souls have to piggyback their communications through the big ships' wormholes, using the very short transit time to fire their communications lasers through the small part of the wormhole opening not blocked by the ship passing through it. There have been serious accidents because people used overpowered lasers and did not calibrate/aim them as they should have. That's why the practice is heavily regulated these days (read: so expensive that it's only a little cheaper than the alternatives). There's still some people who try to do this without a license, but it's dangerous for them because that kind of laser (and its origin) is quickly detected, and it's hard to make sure you're even hitting the correct receiver (and having the correct receiver in place) in such a short time frame. Yet, it's also the most secure way to send data if you don't want the transfer to be registered and logged, since all the other methods are being monitored (to various degrees in different systems, but you never know through which nodes your data will travel).
Potential technical issues
For some of the main planets/outposts etc., there would be fixed locations where the communication wormholes are created, and fixed schedules when which node is connecting to which other node. But if you're on a ship that is moving, potentially along a trajectory unknown to your would-be communication partner, that might be more difficult. Can you initiate communications with a moving ship if you don't know the c-hole (communications wormhole) coordinates for their receiver? Can you initiate contact with a receiver if you don't know its schedule? You might try to open a wormhole while it's trying to receive communications from some other place, and then the wormholes collide, which causes packet loss (possibly in a dramatic way?) and might cause other problems too. Maybe two simultaneous wormholes in one place are a very bad thing, so there would need to be strict administrative and technical measures to prevent that?
Either way, you would probably need to have a "handshake" of some sort to agree on coordinates/wormhole schedule before being being able to establish FtL communications. That means that a spaceship must maintain some sort of communications channel at all times, or they become impossible to contact at all. Except by local communications, of course, which requires a way of getting your message within the range of their sub-light receivers.
For an expedition to an uninhabited system, this would mean that losing their FtL connection would make it impossible for anyone else to reach them unless the expedition manages to reconnect to their base of operations, or you make a much bigger hole and push a communications satellite through (assuming you had one to spare...)
If this is how interplanetary/-stellar communications work, I bet there would be a lot of bureaucracy, regulations, laws, and daily annoyance around it. Whoever operates these devices carries some responsibility, and that means that control of those nodes could (depending again on how hard they are to build and operate) play an important role in politics and economics. Companies/governments controlling and (mis-)using them, outlaws running their own, or some organisations/measures to ensure equal access to secure and safe communications (and the different degrees to which they succeed in that or abuse the trust put in them) could play relevant roles in such a universe.
There would also likely be some communication routes much more popular than others, some wider than others, and some heavily contested/neglected ones. Almost like IRL, where some places get crazy glass fibre speeds but don't really use them, and elsewhere you pay twice as much and still can't have a phone conversation without standing on your kitchen table, so you end up purchasing a freaking expensive satellite link from the richest guy in the known universe...