What is the Copenhagen interpretation of quantum field theory?

I am most interested in interpretational differences due to the fact that quantum field theory is relativistic while quantum mechanics is not. By "Copenhagen interpretation" I mean a minimal interpretation that connects mathematical formalism to observations.

The answer to Collapse in Quantum Field Theory? says:"The collapse of a wavefunction - or its decoherence, or splitting off into different branches as it gets entangled with a measurement apparatus - looks exactly the same". But this is odd. Quantum mechanics has a global time variable, so it makes sense to talk about quantum state at time $t$ being a superposition, and then being a collapsed eigenstate at a later time $t'$. Of course, it turns out that although QM is non-relativistic and collapse is formally "instantaneous", where physical entities are concerned it happens to be compatible with relativity by happy coincidence.

But in a relativistic QFT such description does not work even formally. There is no global time or absolute simultaneity, so no "quantum state at time $t$" that can be described as collapsing. One could try to relativize this to a particular observer, but such "relative collapses" are incoherent because different observers have different simultaneity surfaces. So in QFT instantaneous collapse would not just be formally non-relativistic, but meaningless like a syntax error. So how is the collapse (whether actual or apparent) interpreted in QFT in a way consistent with special relativity?

EDIT: After searching I found Reality, Measurement and Locality in Quantum Field Theory helpful, it analyzes the EPR experiment from the QFT point of view, and discusses collapse explicitly. On interpretational issues of QFT more broadly Against Field Interpretations of Quantum Field Theory gives a nice overview.

Answer

The Born rule (and hence any discussion of collapse in the sense of the Copenhagen interpretation) is relevant only when an observer has made a distinction between a (tiny, observed) system and its (huge, observing) environment (= everything else, containing in particular the measurement equipment).

This distinction (not present in relativistic QFT itself) already breaks Lorentz invariance. The collapse (describing conditional probabilities conditioned on observations) is a property not of the wave functional in QFT but of its restriction to the Hilbert space of the observed system, which is an observer-dependent, vanishingly small part of the Hilbert space of the complete (observed + measuring) system.

This restricted few particle system is only an effective theory, to which fundamental considerations cannot be applied.

Thus there is no contradiction. A sequence of papers with the title Classical interventions in quantum systems by Asher Peres discuss how observations by different observers remain consistent in a relativistic framework.