This reflects just 8.4% of the total Federal prison population.
And the only reason private prisons were "necessary" in the first place is because this same asshat who is now President wrote a crime bill in 1994 that instituted excessive punishments for minor crimes and first time offenders. As a result, the US started jailing so many people that the existing prison system became extremely overcrowded. Then the government put out RFPs for contractors to help them solve that problem.
Private prisons are 100% a creation of the state, and they are 100% paid for by the state. They are also subject to rules and oversight by state boards of corrections. They literally didn't and could not exist outside of government demand. Seriously try to imagine a company just popping up in your neighborhood selling the service they sell. Just like almost everything else that government "privatizes", it's just a government function, still totally controlled by the government, that they've farmed out to contractors to save money.
If you want to see an end to private prisons, you have to put an end to overcriminalization... But why would Biden care about that? He's the reason it's a major issue in the US in the first place, and he'd have to confront the awkward fact that his name is on one of the first bills that would need to be repealed.
This should enrage you far more than anything Trump ever did in the realm of criminal justice. If it doesn't, you need to rethink.