Light sources for applications in quantum information, quantum-enhanced sensing and quantum metrology are attracting increasing scientific interest. To gain inside into the underlying physical processes of quantum light generation, efficient photon detectors and experimental techniques are required to access the photon statistics. In this work, we employ photon-number-resolving (PNR) detectors based on superconducting transition-edge sensors (TESs) for the metrology of photonic microstructures with semiconductor quantum dots (QDs) as emitters. For the PNR analysis, we developed a state of the art PNR detection system based on fiber-coupled superconducting TESs. Our stand-alone system comprises six tungsten TESs, read out by six 2-stage-SQUID current sensors, and operated in a compact detector unit integrated into an adiabatic demagnetization refrigerator. This PNR detection system enables us to directly access the photon statistics of the light field emitted by our photonic microstructures. In this contribution, we focus on the PNR study of deterministically fabricated quantum light sources emitting single indistinguishable photons as well as twin-photon states. Additionally, we present a PNR-analysis of electrically pumped QD micropillar lasers exhibiting a peculiar bimodal behavior. Employing TESs our work provides direct insight into the complex emission characteristics of QD- based light sources. We anticipate, that TES-based PNR detectors, will be a viable tool for implementations of photonic quantum information processing relying on multi-photon states.