Some general thoughts:
While Carney was an adviser of the Trudeau government, I am not inclined to place too much blame for that shit show on him. Trudeau was a moron, and by all accounts ran a PMO that was at the same time authoritarian and sloppy. Carney seems a lot more willing to change direction where required and be pragmatic - time will tell if it's a substantive change but by all accounts he doesn't accept sloppy work from MPs or the civil service.
I also wouldn't necessarily draw conclusions from the fact that he sent his daughter to the Tavistock, at the time that likely would have been what people like GPs and all those in his social circle were reccomending without much exposure to contrary thoughts. I suspect from the form some of his responses to questions have taken that he's followed the debate on this in the UK as it's developed. I have no idea what his personal conclusions about it are but I expect he could outline some of the major points.
Since he's taken office he's been pretty laser focused on economic issues, and has barely mentioned most of the controversial social issues. The economy is undoubtedly the first thing that vast majority of Canadians are really concerned about, the second being immigration, and with a close third being national security issues given Trump's rhetoric, which may not actually be as significant but many people are worried about it.
As far as the big social issues and in particular GI, they are only going to be divisive from Carney's POV, he could not win no matter what he does or says. There is a very long way to go in Canada to get to where the UK is and it may require some significant work in the civil service and within institutions like the CBC, and there is already constitutional protections and god knows how tat will be dealt with. It's instructive I think that even when the Conservatives looked like they would win, they stayed very far away from the trans debate.
Most of Carney's moral authority is being used up, I think, on the immigration issue, because while the vast majority of Canadians think it needs to be addressed there is that contingent within the Liberal Party who see it as a betrayal - he seems to be throwing them the bone of the gun registry, maybe because even though it is stupid he thinks it can only do limited damage. He's even being fairly quiet on indigenous issues.
Some of these things are going to have to be addressed, indigenous issues probably most urgently, and I think GI will become urgent in Canada as the lawsuits and medical issues begin to grow. I would not be shocked to see those as second term questions for Carney. What might be an indicator sooner is what he does about the CBC and civil service, internally. He's trying to rebuild the CBC which has been financially decimated, but will he clean house or try and enforce some real journalistic standards is what I am curious about in the next two years. As far as GI, I hope he will be sensible but by no means confident.