My assumption is that they want to have an outside expert examine the configuration of the routers, which could provide some indication whether or not there was access to the internet, for example. Of course it would be difficult to establish whether or not that configuration had been changed in the meantime, and in my experience a lot of election administrators set up their EMS only on a temporary basis, so I would be unsurprised if supporting equipment like network appliances had been repurposed or returned to a lease provider.

That said, the EMS is usually a small half-rack setup and I'd be surprised for there to be a router at all. Often it's a single machine. The vendors usually tell you to either never connect it to outside networks, or to do so only for setup and disconnect it before you start election preparation. Most, usually all, in-election connectivity to the machines is via sneakernet.

Any kind of detailed network logging becomes a big undertaking at organizational scale, so it's very unlikely that there are any kind of useful persistent traffic logs on the routers. Any such logs would have been kept on a dedicated system like a netflow collector or SIEM, the routers don't have the storage (or storage write endurance). The fact the senate didn't subpoena for such a system suggests it doesn't exist, which is unsurprising. Mass-retention of network traffic logs is a sufficiently expensive and complex thing that not a lot of organizations do it.