I was wrong:

In contrast to the Eugenics Wars having previously been established as taking place in the 1990s, “Doctor Bashir, I Presume”, set in 2373, references the Eugenics Wars as having occurred two centuries prior to the episode, placing the Wars in the late 22nd century. As Ronald D. Moore later admitted, this statement was a production error, a line he had taken from The Wrath of Khan, but he had accidentally forgotten to account for the episode being set a century later than the film.

Source: https://memory-alpha.fandom.com/wiki/Eugenics_Wars