if she instead had been a white male

I feel like the most obvious counterfactual here would be if Biden had kept his faculties and run for a second term - an establishment politician running for business as usual. And I don't think he would have won. His presidency had left people disillusioned with him and seeking something new, and more of the same - regardless of the wrapper - was going to lose. Not to say that a woman of color doesn't face more barriers than a white man - but I don't think those barriers were the determining factor in Harris' loss.