Well Ent J isn't really Enterprise Era. Its supposedly before Star Trek Discovery season 3 and after Picard though unless that timeline was borked.

The Enterprise after Enterprise was supposedly a Daedelus class and then the Connie. The reason they say it was daedelus though is that it was one of the first Uss Enterprise concepts crated by Jeffries and added as a homage but there's no hard core in universe canon to back it up, I've heard also that a Daedelus class starship entreprise was commissioned as a earth fleet vessel and not the Federation which served as a picket and hospital vessel. Until it was retired, Thus Starfleet couldn't use the name.

Can't remember where i heard it, but it's good head canon.