Quantum spin liquids (QSLs) are exotic phases of matter characterized by long-range entanglement and the absence of magnetic order even at zero temperature. Here, we present a comprehensive theoretical study of the frustrated magnet Y${}_3$Cu${}_2$Sb${}_3$O${}_{14}$ to elucidate its electronic and magnetic properties. We uncover completely opposite crystal-field splittings of the two inequivalent Cu sites owing to their fundamentally distinct oxygen coordination - trigonal distorted octahedral CuO${}_6$ and axially compressed CuO${}_8$. This inversion places the unpaired hole in the $d_{z^2}$ orbital at the Cu-2 site, while Cu-1 maintains conventional $d_{x^2-y^2}/d_{xy}$ character, which results in a selective band-renormalization of orbitals from the two Cu ions. We further find multiple magnetic instabilities competing with nearly equal strength in this system: the spin susceptibility lacks dominant peaks, and the leading eigenvalues approach unity simultaneously across all wavevectors with increasing interactions. This competitive interplay, originating from the distinct local environments and geometric frustration on the triangular lattice, agrees well with the absence of long-range magnetic order in experiment. Our results support Y${}_3$Cu${}_2$Sb${}_3$O${}_{14}$ as a promising QSL candidate where the unique combination of disparate crystal-field environments, strong correlations, and competing exchange interactions conspire to stabilize an exotic quantum ground state.