In keeping with canon and/or to make it easier to add into the current ship lineup, they should call it "Ambassador-Class Frigate"
The Constitution-Class was a Heavy Cruiser LOL (check WoK or SfS consoles). So jump ahead 50-60 years (20 years before Galaxy-Class). This ship would be considered of the same type or equivalent. Not sure if Exploration Cruiser replaced the Heavy Cruiser at that time. NEXT: Wesley Crusher in fact called the Enterprise-C a Cruiser in Yesterday's Enterprise; "But that cruiser was destroyed (over) twenty years ago."
And yes the latest news in a Podcast was a story release in Season 7. Two costumes, the Enterprise one and the Probert Concept version. To be fair, I would rather this ship replace the Dakota/Cheyenne/Stargazer, then have a retrofit (Probert Concept) for Tier 5. Makes more sense with all the Excelsior's running around and it being smaller than the Galaxy.