> Among the physicists who do care about the different QM interpretations, it is my understanding that most would go with the Everett (AKA "Many Worlds) Interpretation these days.

In a small poll at a conference on the foundations of quantum mechanics in 2011, the Copenhagen interpretation was the most popular. This could differ from your definition of "these days" I suppose.

https://arxiv.org/pdf/1301.1069.pdf

Update: a 2016 survey by different authors found similar popularity for the Copenhagen interpretation.