You're reading a lot more into the show than is actually there
Could be I've been paying closer attention? That's possible, right?
Here's an exercise for you. For each of the six main cast members of the Discovery, tell me five things about them off the top of your head which don't relate to the plot. You might be able to do it for one or two of them, but I'm guessing not all.
You have guessed incorrectly.
I could, of course, sit here and waste 45 minutes writing an essay about the six major characters on Star Trek Discovery, but I am 99% sure you would just dismiss all of those observations as "plot-driven, doesn't count" no matter what I actually wrote.
The reason is very little has been done to establish the characters exist yet as anything separate from devices to move along the plot.
That's because it's a character-driven plot. Character developments are actual plot points in this story that have lasting consequences for future episodes. This is why Burnham is so horrified with herself for killing Cooper: because she's still carrying the guilt for having "killed him" at the Binary Stars by failing to prevent the war. That's the whole reason why Cooper is even THERE, and it's the whole reason why he tries to kill her in the turbolift. It's not "character development related to plot," the story was written the way it was to drive a development in Burnham's character.
Which is to say, the Mirror Universe is REALLY fucking with her head. That is, in fact, the entire grounding of these stories: the Mirror Universe is a horrible place, not because of what's actually happening here, but because of what it tells Burnham and Lorca (and hell, even
Voq!) about themselves and who they really are inside. What do you think Voq/Tyler's whole "Remain Klingon or die!" tantrum was all about? He literally discovered who he truly is by being confronted with the living embodiment of who he ISN'T.
Of course, Discovery doesn't have compelling, flawed characters who grapple with both internal and external conflicts in surprising and sometimes self-defeating ways, that clearly suffer the (sometimes long-lasting) consequences of their actions and mistakes, so I'm probably just imagining all of it.