The Terrans rebuilt the Connie from the 2260s style into an Eaves-type. Thus, the configuration changed between 2254 (“The Cage”) and 2256 (DSC). We have to disregard the appearances of ‘Q&A’ due to production/asset limitations. The TOS: Early Voyages series correctly depicts the Enterprise era-appropriate.
No they took Eaves' visually rebooted the design, then modified that one into the Terran version.