This was a pretty dope premiere.
Liked the early established character relationships, and threat, the mystery, etc.
Don't know how infer about them ignoring some corrected/established continuity with the appearance of these Klingons. In the OG, they didn't have good enough makeup and costume design so the Klingons basically looked like dark skinned humans with some slight ridges in their foreheads.
Enterprise (which occurs 100 years early) established that Klingons of that time acquired the science and DNA of genetically engineered humans like Khan to improve Klingon warriors and they took on a more human appearance. This would affect a lot of Klingons via breeding and would only decrease over the span of centuries which explains the look of Klingons in the OG Star Trek movies and in the TNG series.
Discovery takes place 10 years before the OG and has Klingons that look like aliens from other movies and even the deformed character Idris Elba played in Star Trek Beyond