The discovery of the most metal-poor stream, C-19, provides us with a fossil record of a stellar structure born very soon after the big bang. In this work, we search for new C-19 members throughout the sky by combining two complementary stream-searching algorithms, STREAMFINDER and StarGO, and utilizing low-metallicity star samples from the Pristine survey, as well as Gaia BP and RP spectrophotometric catalogs. We confirm 13 new members, spread over more than 100°, using velocity and metallicity information from a set of spectroscopic follow-up programs that targeted a quasi-complete sample of our bright candidates (G ≲ 16.0). From the updated set of stream members, we confirm that the stream is wide, with a stream width of ~200 pc, and dynamically hot, with a derived velocity dispersion of 10.9-1.5+2.1 km s‑1. The tension remains between these quantities and a purely baryonic scenario in which the relatively low-mass stream (even updated to a few 104 M⊙) stems from a globular cluster progenitor, as suggested by its chemical abundances. Some heating mechanism, such as preheating of the cluster in its own dark matter halo or through interactions with halo substructures, appears necessary to explain the tension. The impact of binaries on the measured dispersion also remains unknown. Detailed elemental abundances of more stream members, as well as multi-epoch radial velocities from spectroscopic observations, are therefore crucial to fully understanding the nature and past history of the most metal-poor stream of the Milky Way.