JWST has revealed a population of compact and extremely red galaxies at $z>4$, which likely host active galactic nuclei (AGN). We present a sample of 434 ``little red dots'' (LRDs), selected from the 0.54 deg² COSMOS-Web survey. We fit galaxy and AGN SED models to derive redshifts and physical properties; the sample spans z~5-$9$ after removing brown dwarf contaminants. We consider two extreme physical scenarios: either LRDs are all AGN, and their continuum emission is dominated by the accretion disk, or they are all compact star-forming galaxies, and their continuum is dominated by stars. If LRDs are AGN-dominated, our sample exhibits bolometric luminosities ~10⁴⁵⁻⁴⁷ erg\,s⁻¹, spanning the gap between JWST AGN in the literature and bright, rare quasars. We derive a bolometric luminosity function (LF) ~100 times the (UV-selected) quasar LF, implying a non-evolving black hole accretion density of ~10⁻⁴ M_ yr⁻¹ Mpc⁻³ from z~2-$9$. By contrast, if LRDs are dominated by star formation, we derive stellar masses ~108.5-10\,M_. MIRI/F770W is key to deriving accurate stellar masses; without it, we derive a mass function inconsistent with ΛCDM. The median stellar mass profile is broadly consistent with the maximal stellar mass surface densities seen in the nearby universe, though the most massive ~50% of objects exceed this limit, requiring substantial AGN contribution to the continuum. Nevertheless, stacking all available X-ray, mid-IR, far-IR/sub-mm, and radio data yields non-detections. Whether dominated by dusty AGN, compact star-formation, or both, the high masses/luminosities and remarkable abundance of LRDs implies a dominant mode of early galaxy/SMBH growth.
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