The large-scale integration of photovoltaic (PV) generation poses serious challenges of voltage violations and instability risks to active distribution networks (ADNs). To address these issues, this paper proposes a topology-switching soft open point (TS-SOP) assisted real-time cooperative operation framework of ADNs. The proposed framework ensures voltage stability by explicitly incorporating voltage stability margin (VSM) constraints. A TS-SOP model is developed that enhances power flow controllability and reduces standby losses through switchable feeder interconnections and flexible converter operating modes. The proposed framework coordinates day-ahead pre-dispatch, intra-day dynamic correction, and real-time voltage regulation, featuring a two-stage volt/var control. The first stage employs model predictive control to mitigate PV-driven fluctuations, while the second stage embeds VSM constraints into droop curve parameter optimization, ensuring that local droop control actions respect the system stability limits. Simulations on a modified IEEE 33-node system demonstrates that, compared with conventional fixed-topology SOP and droop-only schemes, the proposed framework not only reduces network losses and voltage violations, but also ensures VSM compliance, effectively coordinating fast voltage regulation with system-wide stability while improving the operating economy.