The Fed hire major financial institutions via an open RFP process to run programs all the time, in the same way other government agencies hire outside contractors to run things for them. This makes sense because they do not nececessarily want to maintain the skills, expertise and infrastructure in-house to run these programs themselves. BlackRock is one of the largest asset managers in the world, it makes sense to use them to run an asset management program.
If you want to see another example, during the covid crisis the fed ran a process to decide which custodian to run the Main Street Lending program. They set up the parameters of how it would work and then different custodians could submit proposals ond how they would run it and what their costs would be. This is totally standard for government work of this kind.
https://www.federalreserve.gov/monetarypolicy/mainstreetlend...