You know, that does make me wonder if a lot of the potential criticism towards Burnham's character may ultimately stem from, even while critical of her being correct in hindsight in the episodes, her being deeply wrong in hindsight for the franchise. So for you, as someone new to the franchise, her presumptions as to the inherently violent, war-seeking ways of the Klingons come off as correct based on the information in the first two episodes. To anyone who's seen an episode from TNG on, or so much as glanced at Star Trek VI, they are at odds with both the lore and themes of the franchise at large. Kirk's whole arc in the aforementioned film is realising that, while he has legit grievances against the Klingons, he also cannot allow his specific strain of xenophobia to bar the opportunity for reconciliation, and peace. Compare we get from Burnham with this scene:
https://www.youtube.com/watch?v=hiH1Bk6WmvI
And anecdotally, I have heard that many weren't comfortable with this scene, because it broke the common presumption that the protagonist - particularly in Star Trek - be a morally certain hero. Some of the criticism here does read somewhat similarly - ie, that Burnham is the protagonist, but because her behaviour may be difficult to readily support, some find it hard to accept her character, and therefore, she is an ill fit
as a protagonist.