Her whole problem is that she's a character based on a poorly conceived and terribly executed gimmick.
She's a human child raised by Vulcans. That's supposed to justify her being smarter and all around better than everyone else. But the "trade-off", by the logic of the writers, is that she's meant to constrain her emotions in a non-human way thanks to Vulcan training and culture.
The problem with that is that that doesn't consistently amount to anything except the actress giving serious™ resonant emphasis to every single word and sentence she speaks, as if she was narrating a movie trailer.
She's intonating and emoting (as an actress) the wrong way for her to be taken as Vulcan instead of "tryhard". I wonder if she even watched how Vulcans performed in any other series in order to understand her role. If she put effort into putting NO emotional emphasis in her enunciation, she would probably be a good pseudo-Vulcan, but instead she's putting MORE emotion into her voice and face than any good actor would in any other role.
The other problem with that concept is that the way the story is written is that it's written in such a way as to make her character the centrepiece of emotional drama and expressiveness, all the way through. Burnham is the angry one, the sad one, the suffering one, the one who's in love, the triumphant one, etc etc.
In TOS Spock was a better character because there were more emotional human characters around him for his episodes and character moments to have impact. In STD the only other "tone" given full attention besides hyper-emotional yet emotionally monotone Burnham is goofy, unserious Tilly.
We also have a good basis of comparison with Burnham as well in terms of acting with Seven of Nine. Both characters suffer from the same issue of humans that been raised to suppress their emotions but Jeri Ryan just gives such a more likeable and consistent performance than SMG.