while replaying the trilogy I stumbled upon this:
The normal interstellar communication is provided via FTL Comm Buoys along the Mass Relay network.
For priority messages the point to point QEC's are used.
We do not have Relays in Andromeda, but luckily are bound to a single Star Cluster to begin with, so there might be a Buoy network of some sort shortly after we arrive or better we ourselves install a part of it as Pathfinders.
The Nexus needs to communicate with the Colonies.
As for QEC, my bet is, that every Ark, the Nexus, the Pathfinderships and the biggest Colonies will have one of them, otherwise an immediate report and quick response would be hard.
We know that QEC are not bound to a distance between sender and reciever, Rachni, Levathan, Reapers all had them, otherwise Harbinger would have not been able to assume Control over the General, nor recieved a message that Sovereign failed, but to a specific pair of QEC's.
Though there should be 1 on the Nexus and 1 on the Citadel as a pair, it is save to assume that there is no communication between us and the Milky Way, as the one in the Milky Way has been destroyed in the Reaper War, therefore we only recieve static.
And/or the MW species underwent technologic and biologic advancements in the past 600 years, so their Communication is not primitive anymore and they use Beacons know. But in this scenario Liara rides a huge Mass Relay Construction Ship building a Relay network towards Andromeda.