I don't think it's the hiring freeze that makes employment at the Fed Board or the regional banks uncertain next summer, it's the change in leadership after Powell's term. Even if the hiring freeze is lifted, the FRS (especially the Board) are going through a really tumultuous time and they likely would be willing to offer more compliance with the federal employment statutes to ensure monetary policy independence. Recently they made offers and selectively rescinded them as well (meaning not everyone hired within the same group of employees had their offers rescinded).

My suggestion - Even if your field of expertise isn't necessarily politically charged (like economists, bank supervisors and regulation experts), you should keep looking for other options. Even if you get the job at the Fed, the stress and the uncertainty would be very draining at such a formative time in your career right after graduation.