He is trying to "end the war" on terms that enrich himself, in vainglorious pursuit of a Nobel peace prize, and in a way that will almost inevitably result in a wider conflict very soon. Please don't pretend this is about "people will stop dying". That is utter nonsense.
You were promoted, moved to a flailing team and a new domain. This is a significant career opportunity and people are showing trust in you. I would focus on what is needed in the new area. Somebody else recommended you speak with the senior director who promoted you, to clarify expectations. That is good advice.
Yeah seconding this. If you want to think about it in terms of your resume, putting a bullet point or two to tell the story of how your presence moved that team from not performing to performing well would be very beneficial. That's true even if they're not performing because of social problems, because you might be able to provide the team some alternatives to underperforming. Going above senior engineer is not always about solving the technical challenges, and frankly if you're a staff engineer I would expect you to be willing to dig in on social issues within the team or organization where they hinder your technical initiatives.
When agile first started it was developer centric and brought in the ideas of continuous improvement, inspect and adapt, eliminating waste (handoffs, extra communication etc). One of the core ideas was to look at what was working/not working - if it's not working you drop it. Then we got the scrum cult. Ironically it has led to a huge amount of wasted time and effort, as well as stressed devs. In a lot of cases these extra processes get added by well meaning people who don't look at the whole system of work. If you can't drop what is not working then it's not agile.
