The battle of Procyon V supposedly took place 700 years in the future from Archer's time. That would place it around 29th Century. At that point Klingons were also part of the Federation. It's quite possible that from that war, which spawned across the entire galaxy, a new political body emerged.
The Battle of Procyon V was in the 26th century, and no, that was an alternate future which won't come about. The Enterprise destroyed the sphere network, and the Delphic Expanse, in 2153. Thus the 26th century of prime-Trek will have no Expanse, no Sphere Builders, and no war.