I believe the direct lending program consists mostly of the Fed buying corporate bonds, which is loaning money to private corporations. There is also a component where they can loan to small businesses (notably a business with 200 employees is generally considered "small".
These programs are not handouts, they are loans. The Fed did this in 2008 when they bought bonds and even stock in some big companies.
Overall, the Fed made a big profit on all of that when the bonds were paid back with interest and the stock was sold back in tranches over time as the market recovered.
In any case, I think I was incorrect about the nature of the direct lending program, here is the report from Congress about the CARES Act (the first pandemic relief bill) and how its "expanding the Fed’s traditional role beyond lender of last resort to the banking system and even beyond the more expansive role it took in the 2007-2009 financial crisis"
Its really not a simple "treasury does this, federal reserve does that"
https://crsreports.congress.gov/product/pdf/R/R46329