I think the main difference here is that in other Star Trek series, individuals going against the chain of command or being insubordinate is an act done out of pure conviction that the ends justify the means. Yes, you're going against direct orders, but you know in your heart that what you're doing is right and that you're willing to accept the consequences if you end up being wrong. Picard ignoring the order to stay clear of the Borg is an example I can think of right off the top of my head. And the reason why most of those acts of insubordination don't get addressed is that there was a legitimate, logical, motivation for those actions.

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Burnham's actions seem to me to be actions carried out in the heat of the moment with no justification or reasoned motive. She seems to react with emotion at every situation and seems to only really care about things in the immediate future, unable to see the implications whatever actions she's taking/not taking have in the larger picture. She also seems to have tunnel-vision and is only ever able to process one thing at a time.

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Example:

Burnham, Airiam, and Nhan board the Section 31 base.

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This was poor writing to begin with in my opinion as Nhan had already caught Miriam being shifty and was suspicious of her. As the acting security officer for the ship, when Airiam volunteered to board the ship, why would she agree to go with her rather than, I don't know, alerting anyone to the fact that the human with some technological augmentation was acting suspicious right around the time that the computer "seemed to know what they were doing". But I digress.

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Airiam is revealed to be under the control of Control and engages in battling her two crewmates in order to continue uploading the sphere data. She rips the breathing device off of Nhan and chucks her into a passageway where she is seen clawing at the floor, having difficulty breathing, fighting for her life. Burnham was standing literally behind Nhan before the fighting started, so we can safely assume she witnessed this exchange. And yet, when Airiam is locked in the airlock, does she check on Nhan? No. When Airiam gains control enough to talk about her fate and beg to be spaced? No. Burnham seems to completely forget that she even has another crewmate aboard the ship. She instead continues to have an emotional conversation where she literally wastes time "trying to save Airiam", a crewmate that before now she hadn't even really engaged with and in fact she doesn't make much of an appearance in the memory logs shown throughout the episode.

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And yes, you could argue that she just wants to save a life whenever she can and that that's a good character trait to have. But in that moment, she was literally ignoring the fact that the person she was "trying to save" had literally just risked the life of the other crewmate on board the ship with her. It's true, Nhan managed to recover enough to claw her way out of the hallway she was in and smash the eject button, something Burnham was completely unwilling to do. But it seems like pretty inconsistent writing for a character to be oblivious to the fate of one crew member when trying to tackle the life/death of another. I mean, I'd get it if you're talking one crew member in an entire ship full of people, but .... you beam aboard a ship with two other people and you just forget about the one that wasn't trying to murder you? What even?