We present maps of the stellar streams detected in the Gaia Data Release 2 (DR2) and Early Data Release 3 (EDR3) catalogs using the STREAMFINDER algorithm. We also report the spectroscopic follow-up of the brighter DR2 stream members obtained with the high-resolution CFHT/ESPaDOnS and VLT/UVES spectrographs as well as with the medium-resolution NTT/EFOSC2 spectrograph. Two new stellar streams that do not have a clear progenitor are detected in DR2 (named Hrd and Gunnthr), and seven are detected in EDR3 (named Gaia-6 to Gaia-12). Several candidate streams are also identified. The software also finds very long tidal tails associated with the 15 globular clusters: NGC 288, NGC 1261, NGC 1851, NGC 2298, NGC 2808, NGC 3201, M68, Cen, NGC 5466, Palomar 5, M5, NGC 6101, M92, NGC 6397, and NGC 7089. These stellar streams will be used in subsequent contributions in this series to chart the properties of the Galactic acceleration field on 100 pc to 100 kpc scales.