And this is part of the reason I always shake my head when people get heated about all of this having to fit together in a single continuity. I don't think it would have hurt Discovery or Strange New Worlds at all to have been disconnected from the Prime Timeline. I honestly believe it would have helped these shows to be their own thing.
Doing this would have been good for two reasons.
A) The dedicated fanbase would have had a lot less ‘canon’ anxiety.
B) The nebulous, oft-referred to ‘General Audience’ wouldn’t even notice or care.
It would more easily allow either show to ‘breathe’ and be it’s own thing.