To be fair, in the second article you linked it actually indicates that post-tax inequality increased due to specific COVID era tax breaks expiring, while pre-tax inequality decreased. I think most middle to lower income people are not going to care that their pre-tax inequality is getting better because that doesn't result in a feeling of the boot easing up.
I also think that when many people speak colloquially about wealth inequality they're thinking more in terms of "1% vs 99%" mentality rather than racial income inequality. Not to say that it's not an important metric to monitor, but I think the class divide is more useful to focus on when talking about general income disparities and is what most people mean when they say wealth inequality.
Could Biden do more to help with income inequality? For sure. Will he? Probably not that much. Will he be better for it than Trump? 10000% yes.
Definitely agree it's not really Biden's fault. I think people in general attribute way too much of the state of the economy to the president when it's Congress that is passing the laws that are affecting the most change. Although presidential appointments to regulatory bodies do play a big role and that is something I think Biden has mostly done a good job with and deserves credit for.