How would you hedge interest rate risk on trillions of dollars in US treasuries? Who takes the other side of that trade, and why? I don’t think that sort of hedge exists.
Hedging is done at the portfolio level using derivatives. This allows you to move your unwanted exposure to interest rate risk (or just about any kind of risk) to someone else in exchange for a premium. Whoever is taking that risk off your hands probably has a more diverse portfolio and wants the premium (ie their risk profile is different). In this manner, large fixed-rate creditors shouldn’t be largely exposed to rising interest rates, because they’ve been hedging that risk all along.