Radio observations of stars trace the plasma conditions and magnetic field properties of stellar magnetospheres and coronae. Depending on the plasma conditions at the emitter site, radio emission in the metre- and decimetre-wave bands is generated via different mechanisms, such as gyrosynchrotron, electron cyclotron maser instability, and plasma radiation processes. The ongoing LOFAR Two-metre Sky Survey (LoTSS) and VLA Sky Survey (VLASS) are currently the most sensitive wide-field radio sky surveys ever conducted. Because these surveys are untargeted, they provide an opportunity to study the statistical properties of the radio-emitting stellar population in an unbiased manner. Here we perform an untargeted search for stellar radio sources down to sub-mJy level using these radio surveys. We find that the population of radio-emitting stellar systems is mainly composed of two distinct categories: chromospherically active stellar (CAS) systems and M dwarfs. We also seek to identify signatures of a gradual transition within the M-dwarf population, from chromospheric or coronal acceleration close to the stellar surface similar to that observed on the Sun to magnetospheric acceleration occurring far from the stellar surface similar to that observed on Jupiter. We determine that radio detectability evolves with spectral type, and we identify a transition in radio detectability around spectral type M4, where stars become fully convective. Furthermore, we compare the radio detectability versus spectra type with X-ray and optical flare (observed by TESS) incidence statistics. We find that the radio efficiency of X-ray and optical flares, which is the fraction of flare energy channelled into radio-emitting charges, increases with spectral type. These results motivate us to conjecture that the emergence of large-scale magnetic fields in CAS systems and later M dwarfs leads to an increase in radio efficiency.