2.4uH of inductance stores way too much energy at 10000A, but the idea is that you won't need to ever put 10000A through that 2.4uH! Note the current has a second exponent in the energy stored, so you need to really prevent the current from reaching the resistance-limited short circuit current; act
well before that happens.
Electrolytic caps are cheap and small, it's trivial to store the energy stored in the inductance in the capacitors, unless someone adds a MASSIVE ferrite core in the system, but this wouldn't be expected.
E = 0.5 * L * I^2 = 0.5 * 2.4uH * (550A)^2 = 0.36J
E = 0.5 * C * U^2, solve for C:
C = E/(0.5*U^2). Allow for 20V voltage rise on the capacitor voltage,
C = 0.36J/(0.5*(20V)^2) = 1800uF
You can clamp the voltage to a capacitor bank with a diode even if the switch is bidirectional. The advantage is you may be able to find fast diodes better than extremely fast TVS diodes (I don't know if I'm correct here; you may able to find a directly suitable TVS, as well, in which case the diode-capacitor solution does not have such advantage), and you can discharge the capacitors as slowly as you want.
Note, 2.4uH, whatever this is coming from, is already quite a lot. Using
https://www.eeweb.com/tools/loop-inductance , this would be a circular loop 75cm in diameter. In a properly designed battery pack and wiring, the current and the return current run closer to each other.
The idea is, do not design your active efuse circuit around the short circuit current of the battery, because it sees this current
only if you have failed the design somehow, i.e., it won't be able to detect the overcurrent in time, and switch off the transistors in time - in which case it doesn't matter, it will likely blow up anyway. Instead, design your efuse circuit to prevent the current from ever rising much over the expected maximum operating current. Then, protect (the wire insulation and the battery pack, and other things thermal) against a design failure using a traditional passive fuse, and for that, make sure it handles the 10kA current.