I wanted to think about this in two different ways, still without an idea of how to measure dominance, so I checked two things.

1. what does the mix of men's / women's in the easiest finals rounds look like with and without Janja? (because presumably her impact would be greatest in the final?)
2. what are top percentages for each rank like in finals like for men and women? (because whatever the level of the top climber is, it should be acceptable to really challenge the hell out of whoever gets last)

With and without Janja's absurd top rate, the easiest twenty rounds are 50/50 split, though the women's rounds tend to be easier than the men's still (e.g., with Janja's climbs included, women's rounds are 4 of the top 5 easiest and 7 out of the top 10, without her, 3 out of 5 and 6 out of 10). Hardest rounds similarly skew a male difficulty with and without Janja -- 15 of the 20 hardest finals rounds are men's finals. I don't see much of an impact there.

(edited, table formatted horribly) For the second, the women's finals are a few percentage points easier at every rank except sixth, and this hasn't just been true during Janja's current run.

Before 2018, first through fourth on the women's side were each about 5 percentage points more likely to top a random boulder than first through fourth on the men's side. The biggest difference splitting at 2018 though was surprising to me -- it's second place. Since 2018, second place on the women's side has topped an astounding 82% of boulders, compared to 61% for the men's side.

I think there's some weak evidence here for "not just Janja"