Making of Star Trek and the FJ Tech Manual also called it a Connie.
https://memory-alpha.fandom.com/wiki/USS_Farragut_(NCC-1647)#Background_information
"The following names have been established for starships: Enterprise, Exeter, Lexington, Yorktown, Potemkin, Republic, Hood, Constitution, Kongo, Constellation, Farragut, Valiant, and Intrepid. The latter four are listed as destroyed in various episodes." - The Making of Star Trek, p.165.
As the quote above shows, the Making of Star Trek doesn't say it's Constitution Class, so Memory Alpha is in error here. It says it's a starship, lower case "s". I don't have my copy handy to double check the capitalization, but assuming it is lower case, we need to make a distinction between "starships" and "Starship Class" ships. The Farragut and Valiant can be the former without being the latter.
That sort of confusion might be why the name was changed to "Constitution" in universe. My personal head canon being that Starship Class ships are named after famous historic starships, until people started getting confused and the class was renamed Constitution after the first built ship.