This paper studies a pinching antenna system (PAS)-assisted hybrid uplink architecture that integrates over-the-air computation (AirComp) and non-orthogonal multiple access (NOMA) to simultaneously support distributed data aggregation and individual communication services. A base station with a dielectric waveguide hosting multiple pinching antennas receives signals from AirComp and NOMA users over shared time-frequency resources. To assess joint computation-communication performance, a hybrid metric combining the AirComp computation rate and the NOMA sum rate is proposed. Based on this metric, a joint optimization problem is formulated to maximize the hybrid rate by optimizing user transmit precoding, receive combining, and antenna deployment, subject to power, quality-of-service, and aggregation accuracy constraints. An alternating optimization framework is developed to solve the resulting non-convex problem. Numerical results show that the proposed design achieves significant performance gains over several benchmark schemes.