I also just saw the first couple of episodes. (On US TV, the first couple were free on CBS and then the rest you had to get a subscription to an online channel or something.) I started watching partway into one episode, and I kept waiting for the moment when the crew would discover that the enemies they were fighting were not Klingons, but some new strange race.
And slowly it dawned on me that they were Klingons.
This left me confused for awhile, and then I discovered some quotes from the producers of the show about this. They seemed to be very proud of themselves for turning this cardboard, superficial enemy race into one with a unique and interesting culture. Which left me confused, because of course the Klingons had been very deeply fleshed out in the movies and the later series, so much so that some of the very best work in those later shows was Worf's interactions in the complicated political and cultural world of the Klingons. In fact, one could argue that the new show was a step in the wrong direction, as it kind of borrowed some overdone tropes in an attempt to paste on a new story for the Klingons.
Which again made no sense. Star Trek writers have never been shy about introducing new races. TNG gave us the Borg and the Bajorans and the Cardassians, Deep Space Nine gave us the Vorta, Voyager gave us a host of Delta Quadrant races. If you think you have a cool idea for a deep alien culture that Star Trek hasn't explored, why not make a new race? Why paint over the brilliant (and fan-loved) work done by previous Star Trek universe builders? It just made no sense. Either embrace the universe or do something different... don't sort of embrace and then fuck with it.
In fairness, Star Trek did do this once before. I adored the original series Romulans - a very interesting characterization of duty and honor. I can't say I adored the Klingons, as they really were at that time cardboard villians. But when the movies and TNG came out, the Romulans became the dirty bastards who don't play fair, and the Klingons became the ones with a rigid code of tradition and duty and honor. However, given the massive improvement of the physical appearance of Klingons between TOS and TNG, that was much more forgivable. The change in the physical appearance from TNG to Discovery was just goofy.
I also react negatively to this notion of "alternate timelines". The latest batch of Star Trek movies with the young original crew did not sit well with me. The massive plot holes were bad enough, but just the idea that I'm supposed to still be invested in these characters even though they are alternate timeline versions of these characters just doesn't make sense. Either tell more stories in the universe I'm familiar with or give me some interesting characters in a brand new universe. Alternate timelines are just an excuse for really lazy writing.