Excellent questions, occasionally asked by others and me--with no formal responses.
Publicly, FHFA doesn't designate and if it did honestly, they would have some level of employees in both categories. Nobody on the Hill knows and if anyone in government does, it might be OMB but its knowledge would come from the agency and therefore be subject.
It's a good question to get some Senator to ask Ms. Thompson when she appears for her Senate confirmation.
He/she might also ask Ms.Thompson to identify just how many people FHFA has (rumored to be over 700), their titles and functions, and their growth rate over the past three years (Calabria era).