The whole concept of 'reactive power' comes from trying to extend concepts that are true only for _DC_ or _instantaneous_ measurements to AC circuits.
We take the concept of Amp, which applies to DC circuits, and come up with the measurement 'Amp RMS' and apply it to AC circuits.
We take Volt, which applies to DC circuits, and come up with 'Volt RMS' and apply it to AC circuits.
For _DC_ or _instantaneous_ measurements, Volts * Amps = Watts.
But V(RMS) * A(RMS) does _not_ equal Watts(time averaged). We introduce the concept of reactive power and power factor to maintain the utility of RMS measurements.
When you are not looking at time averages, there is no such thing as reactive power.
When you connect a power supply to an electromagnet, then _real_ power flows to create the magnetic field. _Real_ energy is stored in that magnetic field.
If you connect a load to that electromagnet and disconnect the power supply (something done with diodes all the time in switching power supplies), then _real_ power flows as the magnetic field collapses, and _real_ energy is delivered to the load.
If you connect a capacitor to an AC supply, then _real_ power flows to the capacitor for 1/4 cycle, and _real_ power flows from the capacitor back to the supply for 1/4 cycle. This is _real_ energy being shuttled back and forth. (Since this power flows for a fixed amount of time, it is a defined amount of energy.) If you were to intercept back and forth shuttling (another example: a voltage multiplying circuit using diodes and capacitors) then _real_ power will flow to a load. The same shuttling applies to an inductor connected to an AC supply.
It is only when looking at the time average values, where we want to account separately for the power flowing to the load and the power shuttling back and forth then we see 'reactive power'.
It may be reasonable to call energy stored in a magnetic field 'reactive energy', but that is _real_ energy which could be used to do real work. Only when that energy is returned to the supply on a cyclic basis to we call it 'reactive power'.
-Jon