JWST has revealed an abundance of low-luminosity active galactic nuclei (AGN) at high redshifts (z > 3), pushing the limits of black hole (BH) science in the early Universe. Results have claimed that these BHs are significantly more massive than expected from the BH mass─host galaxy stellar mass relation derived from the local Universe. We present a comprehensive census of the BH populations in the early Universe through a detailed stacking analysis of galaxy populations, binned by luminosity and redshift, using JWST spectroscopy from the CEERS, JADES, RUBIES, and GLASS extragalactic deep field surveys. Broad Hα detections in 31% of the stacked spectra (5/16 bins) imply median BH masses of 105.16─106.08 M⊙, and the stacked spectral energy distributions of these bins indicate median stellar masses of 107.84─108.56 M⊙. This suggests that the median galaxy hosts a BH that is at most a factor of 10 times overmassive compared to its host galaxy, and lies closer to the locally derived MBH─M* relation. We investigate the seeding properties of the inferred BHs and find that they can be well explained by light stellar-remnant seeds undergoing moderate Eddington accretion. Our results indicate that individual detections of AGN are more likely to sample the upper envelope of the MBH─M* distribution, while stacking of "normal" galaxies and searching for AGN signatures can overcome the selection bias of individual detections.