Nice post.
Obviously it's about conditions. Tuchel at PSG is doing more in Europe than at PSG,not because Tuchel changed, it was the conditions that changed.

Rangnick at Milan would have been different from this version of Rangnick because,the United environment he met was toxic with a cold war kind of thing amongst some players. A situation which he wouldn't have had if he was in Milan.

Well it has benefited Pioli and the man is using the opportunity afforded him very well.

Getting results is crucial in football and even in all of life. Pioli gave himself a chance for the job by focusing on the job,even when it was clear Rangnick had an agreement to take over from him. That focus gave him impressive results(like you have talked about above) and the rest is history. Kudos to him.