in addition to what Lubos said about QM, the philosophy of axiomatic QFT is to construct/describe QFTs without any reference to concepts of classical physics. As far as I know there is not even a concept for a "classical limit" in axiomatic QFT. Especially "macroscopic classical" devices like detectors are modeled in AQFT via an observable, that is a selfadjoint operator, and that is a pure quantum concept. Therefore I don't think that you'll find a formalization of something like the "Heisenberg cut" in axiomatic QFT.

As for the interpretation of the measurement process etc., this is usually left to the philosophical interpretation of QM, from a pure philosophical point of view there is no conceptual difference of the interpretation of QM and that of QFT, which is the reason why most people working on this topic concentrate on the technically much simpler QM.

In addition to what Lubos said about QM, the philosophy of axiomatic QFT is to construct/describe QFTs without any reference to concepts of classical physics. As far as I know, there is not even a concept for a "classical limit" in axiomatic QFT. Especially "macroscopic classical" devices like detectors are modeled in AQFT via an observable, that is a selfadjoint operator, and that is a pure quantum concept. Therefore I don't think that you'll find a formalization of something like the "Heisenberg cut" in axiomatic QFT.

As for the interpretation of the measurement process etc., this is usually left to the philosophical interpretation of QM, from a pure philosophical point of view there is no conceptual difference between the interpretation of QM and that of QFT, which is the reason why most people working on this topic concentrate on the technically much simpler QM.