Disregarding what we've already since found out about McKinnon here, I did just pop on that relevant section of the video to see what the fuss was about. Like many of theses 'deep dive' videos about a subject it's just one guy with an enthusiastically-held opinion he's happy to share without any supporting data, just what he's read and decided to pass on. There's lots of negative characterisations about how things happened, but he gives no indication how he knows any of it, beyond I assume having read the Eagleton book where all this stuff originates from.
So I went and had a look at that, and it seems that the entire source for what that book talks about with regard to McKinnon is what his mother told Eagleton in an interview. I'm sure she's got her unique insights into it, but she's far from an unbiased observer and the one quote they can attribute to Starmer about being "uncomfortable" when she confronted him directly is understandable from the context of being a prosecuting lawyer in communication with a party to the defence, presumably without the corresponding defence lawyer present.
Any additional details the book mentions about him "Furiously flying to Washington immediately and apologising to his US counterparts" aren't referred to at all by any of the reporting at the time I've seen and from the reviews of the book are mainly supported by Starmer himself not bothering to deny it. Given I'd not heard of this book or author until today that might well be because Starmer didn't want to give it the dignity of a response.
It could all be true, but the basis of it is a book written by someone openly hostile to Starmer, featuring an interview with someone with a good reason to have a negative view of him and his involvement in a case she was very close to and emotionally involved with.