How does educational modality shape the social organization of student life? While the structural consequences of face-to-face versus screen-to-screen instruction have attracted scholarly attention, direct evidence on how this transition reshapes student social networks remains limited. Drawing on complete transcript records and network data from Korea University in 2019 (N=21,607) and 2020 (N=21,572), this paper analyzes co-enrollment networks before and after the shift to online education. The COVID-19 pandemic offers a rare quasi-natural experiment for this investigation. Despite the pandemic disruption, the macro-level architecture of co-enrollment networks proved resilient, preserving small-world properties with comparable levels of connectivity, clustering, and degree assortativity. Beneath this structural stability, however, online learning quietly reorganized the mechanisms of network formation; residential proximity and academic performance emerged as stronger bases of assortative sorting, while disciplinary and cohort boundaries remained largely unchanged. Most strikingly, GPA-based assortativity increased even when self-evaluation-based assortativity declined—suggesting that online learning simultaneously amplifies institutional measures of academic standing while eroding the social salience of students' subjective academic identities as an axis of sorting. These findings reveal a fundamental paradox. Rather than dissolving social boundaries, online education appears to have reinforced stratification along residential and performance lines.