I agree the Tilly discussion is played out...so let's shift to the other crucial flaw in the episode.
Michael has an important realization at the climax of the episode: That it's not really all about her and the monomania she has regarding the Burn. She steps back from the precipice when she has the chance to push for the "needed" data, when she realizes that making such a request will spark civil war. It's left unsaid, but it seems she realized that her mission as a Starfleet officer - which was in part to attempt to re-establish normal relations with Ni'var - was more important than her silly quest. So she puts on her big girl pants and says no thank you, showing an amazing level of emotional growth.
Then the episode rewards her by handing her the needed data anyway.
Narratively speaking, this is a terrible, awful decision, which completely undercuts her character growth. Choices should have consequences, and she basically got out scot-free from the "hard choice" that was put in front of her. She got to complete her Starfleet mission and got the data. The conclusion she will draw from this is that she's always right - it just so happens this time around she was right to fold. But she can continue to do what feels right to her in the moment and suffer no repercussions.
The worst part about all of this is it was entirely unneeded in terms of narrative. The episode could have ended on a strong bit of character growth, and Michael could have just noted in the opening of the very next episode they managed to get somewhat analogous information from some other source. So we didn't need to have Momma Burnham pass along the data at all. The episode would have had such a strong finish - possibly the strongest of the entire series - if they had just done this.