At the moment, calling NetworkService::write_notifications synchronously verifies whether we have a connection with the peer, and if so sends a message on a channel in destination to the background task of this specific peer.

The problem is that this channel is already quite overloaded, and we should ideally try to reduce the traffic on this point of contention.
Additionally, we can't properly implement #5481 with this system.

Instead, there should be a field in NetworkService (not NetworkWorker) that directly contains channels whose receiving side are the background tasks.