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Optically active defects in 2D materials, such as hexagonal boron nitride (hBN) and transition metal dichalcogenides (TMDs), are an attractive class of single-photon emitters with high brightness, room-temperature operation, site-specific engineering of emitter arrays, and tunability with external strain and electric fields. In this work, we demonstrate a novel approach to precisely align and embed hBN and TMDs within background-free silicon nitride microring resonators. Through the Purcell effect, high-purity hBN emitters exhibit a cavity-enhanced spectral coupling efficiency up to $46\%$ at room temperature, which exceeds the theoretical limit for cavity-free waveguide-emitter coupling and previous demonstrations by nearly an order-of-magnitude. The devices are fabricated with a CMOS-compatible process and exhibit no degradation of the 2D material optical properties, robustness to thermal annealing, and 100 nm positioning accuracy of quantum emitters within single-mode waveguides, opening a path for scalable quantum photonic chips with on-demand single-photon sources.