The Fed isn't equipped to do security selection so that's why Blackrock is managing this facility. Blackrock is absolutely going to do secondary bond purchases (on the Fed's behalf) once that portion of the facility is up and running.

The Fed has also said that they don't want to influence market share of ETFs so that's been interpreted as some sort of benchmark per manager. I believe Blackrock was around 50% of qualifying ETFs outstanding at the time. The Fed published purchases to date last week which has a pretty decent breakdown: https://www.federalreserve.gov/monetarypolicy/files/smccf-tr...