Just had this discussion in my annotations post. My take is that it’s a civilian ship, as you suggest. Not necessary a cargo freighter, just not part of the United Earth Fleet.

It could be a US ship. Perhaps the civilian ships retain their national status and only the military is unified under the United Earth Fleet.

What gives? Was the Iowa was a cargo ship? Maybe in this timeline, “USS” stands for “United Shipping Service.” Or perhaps at some point, UEF ships did use the prefix and they changed it because the wanted “Earth” more clearly in the identifier.

Maybe it's a case of Starfleet vs United Earth? There was a rebranding sometime down the line, similar to how Earth is one of the few Federation powers that doesn't maintain its own spacefaring force.

Does it make sensé to have ships from country when earth IS a complété wasteland apparently?

There are a bunch of ship prefixes in Star Trek for ship..."We" just mostly see Starfleet Ships. In the OS the first season had a bunch

I'd guess the United Space Ship Iowa was a "Residential ship": A ship for families to live on. Though it could also be a cargo ship, like the ones seen in ENT.

We do not know when the UEF was formed. It could be a relatively new initiative having taken longer to get started without the help of the Vulcans. The USS Iowa is a United States Starship whereas the UEF Enterprise is the United Earth Fleet ship. Sometime between Kirk's birth and the 'present' Earth was finally able to form a central government (or at least a centrally organized spacefleet) under one banner.