A global understanding of Active Galactic Nuclei (AGN) and their host galaxies hinges on completing a census of AGN activity without selection biases down to the low-luminosity regime. Toward that goal, we identify AGN within faint radio populations at cosmic noon selected from new ultra-deep, high resolution imaging from the Karl G. Jansky Very Large Array at 6 and 3 GHz. These radio data are spatially coincident with the ultra-deep legacy surveys in the GOODS-S/HUDF region, particularly the unparalleled Chandra 7 Ms X-ray imaging. Combined, these datasets provide a unique basis for a thorough census of AGN, allowing simultaneous identification via (1) high X-ray luminosity; (2) hard X-ray spectra; (3) excess X-ray relative to 6 GHz; (4) mid-IR colors; (5) SED fitting; (6) radio excess via the radio-infrared relation; (7) flat radio spectra via multi-band radio; and (8) optical spectroscopy. We uncover AGN in fully half our faint radio sample, indicating a source density of one AGN arcmin$^{-2}$, with a similar number of radio-undetected AGN identified via X-ray over the same area. Our radio-detected AGN are majority radio-quiet, with radio emission consistent with being powered predominantly by star formation. Nevertheless, we find AGN radio signatures in our sample: $sim12%$ with radio excess indicating radio-loud activity and $sim16%$ of radio-quiet AGN candidates with flat or inverted radio spectra. The latter is a lower limit, pending our upcoming deeper 3 GHz survey. Finally, despite these extensive datasets, this work is likely still missing heavily obscured AGN. We discuss in detail this elusive population and the prospects for completing our AGN census with JWST/MIRI.