We present results from a 3.2 kg-day target exposure of two 24-megapixel skipper charge-coupled devices (CCDs) deployed in the DAMIC setup at SNOLAB. With a $10\times$ reduction in pixel noise, 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 observed energy spectrum and spatial distribution of ionization events with electron-equivalent energies ${<}500$ eV confirm the presence of a bulk excess compatible with previous findings. This measurement establishes the existence of a prominent source of low-energy events in the CCD target with characteristic rate of ${\sim}7$ events per kg-day, and energies ${\sim}80$ eV, whose origin remains unknown.