The possibility of measuring neutral-current coherent elastic neutrino¿nucleus scattering (CENNS) at the TEXONO experiment has opened high expectations towards probing exotic neutrino properties. Focusing on low threshold Germanium-based targets with kg-scale mass, we find a remarkable efficiency not only for detecting CENNS events due to the weak interaction, but also for probing novel electromagnetic neutrino interactions. Specifically, we demonstrate that such experiments are complementary in performing precision Standard Model tests as well as in shedding light on sub-leading effects due to neutrino magnetic moment and neutrino charge radius. This work employs realistic nuclear structure calculations based on the quasi-particle random phase approximation (QRPA) and takes into consideration the crucial quenching effect corrections. Such a treatment, in conjunction with a simple statistical analysis, shows that the attainable sensitivities are improved by one order of magnitude as compared to previous studies.