That's incorrect.In plain quantum mechanics. The energy and momentum are in the hamiltonians of the wave function.
QM is a theory about observations. It only has properties like energy or momentum when its observed to have those properties. To determine the statistical outcome of those observations you need both the observable and the state then you use the Born rule. A QFT field is as real or not real as any observable in QM. It's not real in the sense of having that value - it is real in the sense it allows us to determine things that are very real - observations.