Asking, there are 2 court systems in the US. The Federal system which handles federal crimes and the State system which handles a particular individual state's crimes. The charges are in this case are federal crimes so they will be prosecuted in the US Federal Courts for the Eastern District of Virginia (the federal courts nearest where the alleged offenses occurred).
As Attorney General, Barr is 'in charge' of the entire federal court system. So Barr theoretically has the final 'say so' as to whether or not this case goes forward. Normally, that decision would be made by the Asst AG for the Eastern District of Va, but Barr can always, ahem, 'take an interest', if he chooses to. Although I am very sure there are going to be a LOT of eyes peeled on this case to be sure all the 'i's are dotted and the 't's crossed. Not that that seems to mean much these days, though.
I'm not so sure about Barr Hear. After his sycophantic 'opinion paper' re the 'illegality' of the Mueller Investigation it's hard to tell how far he'd allow himself to be compromised.
From your mouth to God's ear lion.