This paper develops a novel machine learning-based framework using Semi-Supervised Multi-Task Learning (SS-MTL) for power system dynamic security assessment that is accurate, reliable, and aware of topological changes. The learning algorithm underlying the proposed framework integrates conditional masked encoders and employs multi-task learning for classification-aware feature representation, which improves the accuracy and scalability to larger systems. Additionally, this framework incorporates a confidence measure for its predictions, enhancing its reliability and interpretability. A topological similarity index has also been incorporated to add topological awareness to the framework. Various experiments on the IEEE 68-bus system were conducted to validate the proposed method, employing two distinct database generation techniques to generate the required data to train the machine learning algorithm. The results demonstrate that our algorithm outperforms existing state-of-the-art machine learning based techniques for security assessment in terms of accuracy and robustness. Finally, our work underscores the value of employing auto-encoders for security assessment, highlighting improvements in accuracy, reliability, and robustness. All datasets and codes used have been made publicly available to ensure reproducibility and transparency.