Actually FBI background checks of potential appointees require voluntary cooperation of the applicant. The potential appointee has to fill out a form granting permission, and providing basic information to start (financial, personal, employment, affiliations, etc).
It isn't clear from the stories on this whether Trump and his team will be requiring appointees to consent to a FBI evaluation, or what the consequences would be if they don't. (Normally the response would be "thank you for your interest, but without this background check you can't be named to this position"
Of course, the Senate can order their own background check from the FBI.
Wow. Trump will berate him constantly. Will DeSantis eat shit for four years to get his shot at 2028? Yes, yes he will.
But, Florida's loss is Florida's gain.