There are few people that I can not sympathize with on some level, save for egregious criminal or immoral behavior. So, Burnham is someone I sympathize with because she presents as a very traumatized individual who was then raised not to deal with the trauma but to suppress it. So she had to relearn and become better.
To me that's about as Star Trek as it comes.
I think I'm just exhausted from seeing characters like this because it mirrors real life, and for me, fiction should help you escape more than remind you of reality, although you can still learn something about yourself and others if the fiction is done well.
Maybe it's the style of acting Green chooses that bugs me? The whisper-talking, which might be more of a result of modern technology than anything else. Better mics, etc. Somebody else here mentioned how the camera moves a lot in Discovery, maybe Picard and SNW, too, but the actors rarely do at the same time, which is something I've heard Berman didn't want in the shows he ran. The actors must be doing things and not just standing/sitting there like bumps on a log. I know the modern way of filming is more cinematic and perhaps that's the ultimate issue for me: Star Trek used to look a certain way, and that all changed after 2005, I'd say even more dramatically than when TNG premiered.
Also, aside from SNW, the episodic format has largely been dropped in favour of serialization, seasons are much shorter, and these things if not carefully balanced, which I think Lower Decks and Prodigy do wonderfully, will limit character and story development. I also think DISCO and PIC had multiple showrunners, which also didn't help smooth things out.
As I said above, Discovery unfortunately doesn't exceed the sum of its parts for me. Same with Picard, season 3. But I'll continue to watch new outings as long as I can because I'm a fan of the franchise. I only wish I could love all of it.