I think there's a confusion of terms here. You're defining left and right "wingness" based on political party affiliation. In which case, I'm not aware of Harris advocating for Republican candidates, though I don't follow him.
But the author is likely considering Harris' broader world view, which as sibling commenters have noted, is full of race realism, clash of civilizations narratives, and other distinctly right-wing ideas.
It might be instructive to consider Jordan Peterson. Peterson and Harris are similar in a lot of ways; they travel in similar circles, they both use academic credentials to give authority to their political views, they have similar views on trans people. They both buy into debunked myths about IQ. They both talk a lot about "waking up," Harris through meditation and Peterson through cleaning your room.
For years he and his supporters insisted that he wasn't a right-winger. Now Peterson is on The Daily Wire. I doubt we'll see Harris pursuing a similar path, Harris seems much less erratic. But I think it's an interesting parallel.