The prose makes it pretty clear that David Mack was visualizing "The Cage" look for the
Enterprise and its crew's costumes, while DSC and the
Short Treks all show the Disco-prise designs were already in use -- although, to be fair, the mere existence of the Diso-prise is a huge "Continuity Snarl" that's there's no good in-universe answer for (from a certain point of view, Mack got it right, and DSC got it wrong

). Course, since the novel format doesn't have pictures, it does soften the "error," since we don't literally see things the way we do with a TV show.
The Enterprise War does its best to reconcile
Desperate Measures with the rest of DSC. The level of success can be debated, but I think it's the best we could expect, under the circumstances.
I seem to recall that John Jackson Miller indicated in a interview that he planted a throwaway line to imply that the Disco-prise was a temporary refit exclusive for the mission they were on in the book. That would be as elegant a solution as any, although the
Short Treks muddied things with anochronistic Disco-prise sightings (but, thankfully, the line was vague enough that there isn't a continuity error beyond the Disco-prise situation as a whole.