I don't think you need to watch Discovery to enjoy Strange New Worlds.
There might be a few things established in the lore/backstory from Discovery, but any "confusion" from those references will quickly dissipate. SNW makes it easy to see it as a distinct show in a new/expanded telling of a known crew/time.
I will add that there will be stylistic choices in the production that will take a little getting used to, but remember that just about every Star Trek show has done this. Enjoy the story!