We present results from a 3.1 kg-day target exposure of two skipper charge-coupled devices (CCDs) deployed in the DAMIC (DArk Matter In CCDs) experiment at SNOLAB. With a reduction in pixel readout noise of a factor of 10 relative to the previous detector, we investigate the excess population of low-energy bulk events previously observed above expected backgrounds. We address the dominant systematic uncertainty of the previous analysis through a depth fiducialization designed to reject surface backgrounds on the CCDs. The measured bulk ionization spectrum confirms with higher significance the presence of an excess population of low-energy events in the CCD target with characteristic rate of ∼7 events per kg-day and electron-equivalent energies of ∼80 eV, whose origin remains unknown. The confirmation of this excess population has significant implications for the next generation of CCD dark matter experiments. We explore two hypothetical scenarios for the observed excess, considering it both as an irreducible background and as a manifestation of new physics.