  Floquet theory and other established semiclassical approaches are widely used
methods to predict the state of externally-driven quantum systems, yet, they do
not allow to predict the state of the photonic driving field. To overcome this
shortcoming, the photon-resolved Floquet theory (PRFT) has been developed
recently [Phys. Rev. Research 6, 013116], which deploys concepts from
full-counting statistics to predict the statistics of the photon flux between
several coherent driving modes. In this paper, we study in detail the scaling
properties of the PRFT in the semiclassical regime. We find that there is an
ambiguity in the definition of the moment-generating function, such that
different versions of the moment-generating function produce the same photonic
probability distribution in the semiclassical limit, and generate the same
leading-order terms of the moments and cumulants. Using this ambiguity, we
establish a simple expression for the Kraus operators, which describe the
decoherence dynamics of the driven quantum system appearing as a consequence of
the light-matter interaction. The PRFT will pave the way for improved quantum
sensing methods, e.g., for spectroscopic quantum sensing protocols,
reflectometry in semiconductor nanostructures and other applications, where the
detailed knowledge of the photonic probability distribution is necessary.
