Refit has been used very loosely in Picard especially with the Stargazer and now Titan. A true refit wouldn't need a new registry number IMO.
If the Titan-A is a Refit than IMO it's not an upgrade version of Riker's Titan which was a Luna Class Vessel but an upgraded version of the original Titan from the 23rd Century which was Shangri-La Class which the Neo Constitution is based off.