My reading of that literature is that there isn't a lot of evidence one way or another. However, last time I looked at it it seemed like the most likely cause was from how some mates are smoked, and that unsmoked mate didn't have the same cancer risk. Take this with a grain of salt though, because although I followed that pretty closely for awhile, I stopped at some point and it's been a couple of years since.

Any source of what brands/varieties are smoked vs not?

I’m able to get quite a few types imported from South America, but from my attempts at translating the packaging and trying to Google things, I can’t tell what’s smoked or unsmoked.

Argentinian mate is traditionally smoked so most brands you will find are of the smoked variety. The brazilian version, chimarrão, is traditionally not smoked, so you might start by looking for that.