The increasing penetration of renewable energy introduces more uncertainties and creates more fluctuations in power systems. Conventional offline time-domain simulation-based stability assessment methods may no longer be able to face changing operating conditions. In this work, a graph neural network-based online transient stability assessment framework is proposed, which can interactively work with conventional methods to provide assessment results. The proposed framework consists of a feature preprocessing module, multiple physics-informed neural networks, and an online updating scheme with transfer learning and central moment discrepancy. The t-distributed stochastic neighbor embedding is used to virtualize the effectiveness of the proposed framework. The IEEE 16-machine 68-bus system is used for case studies. The results show that the proposed method can achieve accurate online transient stability assessment under changing operating conditions of power systems.