I think Burnham is competent but mired by her own self-loathing and doubt.
I think Burnham utilized her knowledge of both Sarek and the Klingons without letting her personal hurts get in the way at the end. Now, did some things go lucky? Yeah, a bit, but even that was unpacked in Season 2 with L'Rell having to sort out the consequences with the Council.
My understanding of what the writers were attempting to tell us during Season 1's first half was essentially that Michael was someone in deep denial about who she was. She was raised by Sarek to be "culturally Vulcan" and thus always believed she was acting from cool, collected rationality. But the combination of her human biology and trauma meant she was in fact a very impulsive, emotional individual who came up with after-the-fact rationalizations for her random-ass decisions. So her desire to give "the Vulcan Hello" to the Klingons was not coming from a position of logic, it was coming from a position of terror. Over the course of the season she gets more centered regarding her emotional core (never mind how she was on the Shenzhou for 10 years or whatever and showed no growth then). By Into the Forest she seems somewhat calm and collected, even though she's back on the Ship of the Dead. Indeed, she is the one who has to comfort Ash when he is falling apart.
But nothing they did in the MU followed up on this really - it was just emotional torture. And she just kept right on making random-ass impulsive decisions (like saving MU Emperor Georgiou) all the way through to the end. So thematically the ending didn't work for me, because I think the proper end for the season in order to show she had growth would be for her to not trust her instincts for once. Maybe actually listen to orders from a commanding officer, or take advice from Saru or something that cut against what she thought was the right decision? Instead the ending seemed to imply her real mistake was being a warmonger, which fit with none of the real themes of the season and her character.