However the elephant in the room at least for aviation is that the energy per kg is about 50 higher for kerosene than for lithium batteries. A very large part of an airliner is fuel already. 50 as much? Not gonna happen. This will remain a really short range thing unless a really amazing breakthrough happens.
One can imagine regenerative braking in the fans, for example to recover energy as aircraft descend, and also with batteries providing emergency backup power.
Aircraft typically operate at 80-100% power output. It’s not the average 20% power output of your car.
Weight is pretty much everything, the savings from regenerative braking in an aircraft are almost 0% but the cost of enabling it is some tons.
This tech makes loads of sense in a car but I’ve never flown an aeroplane in stop-start traffic because that’s not how the sky works.
PS I'm a hobby pilot so please correct me if I'm wrong but I don't think even an airliner would idle their engines during descent.
An airliner will use maximum power at takeoff, somewhat less for climbing, and much less during cruise. The figure I see is takeoff fuel consumption/hour is like 3x cruise fuel consumption/hour. Power needed will also decline as fuel is burned off, since the required lift goes down.