I mean is the formula taken as a postulate or can we derive it from QFT at least?
Einstein derived it from SR first because he discovered/developed SR before QFT was developed.
There is a certain historical order in which discoveries have been made, which is separate from what we may consider to be the logical order in which things should be developed.
For instance, Archimedes played around with the concepts of the infinitesimal calculus centuries before number systems and algebra were developed, when only arithmetic was crudely understood.
This is not to say that energy-mass equivalence may not be developed using QFT (I can't say because I am not a quantum mechanic), but that's not how it happened first.
QFT is usually started by postulating some field Lagrangian which is assured to be relativistic by design. So we cannot really be surprised when we find out that the particles obtained by quantizing the fields also turn out to obey fully relativistic relations, can we. In other words, we feed our knowledge that the world is relativistic into the theory from the get go.
Special relativity is nothing that is tied to classical physics. And quantum field theory doesn't need to be relativistic either. It's wrong to think about special relativity as something classical that has to be carried over to QFT. Instead, it is a basic insight about space and time that applies equally to classical physics and to quantum physics.Exactly. Usually newer theories include the older ones as a limit. But in this case it is curious that supposedly QFT our most advanced tool that probes nature depend on a semi-classical theory for its survival. You would expect the opposite wouldn't you?
Special relativity is nothing that is tied to classical physics. And quantum field theory doesn't need to be relativistic either. It's wrong to think about special relativity as something classical that has to be carried over to QFT. Instead, it is a basic insight about space and time that applies equally to classical physics and to quantum physics.
... we cannot apply GR to QFT even so GR is considered to be the generalization of SR.
is not correct. Yes, many theories (all candidates I have listed above) try to quantize GR. But the conclusion that this quantization results in SR (in some limit) is not correct. SR is already present in classical GR, but only as a local (instead of a global) symmetry. Spacetime in GR need not have any global symmetry at all, but is always has local Lorentz invariance by construction. This is nothing else but the famous equivalence principle. A free-falling observer cannot detect spacetime curvature locally; to her spacetime always looks flat. So for local experiments a free-falling observer can always use SR calculations.... many theories of QG try to consider GR as a quantum theory which implies that the origin of SR is indeed in QM system somehow.