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Since the COVID-19 pandemic, online courses have expanded access to education, yet the absence of direct instructor support challenges learners' ability to self-regulate attention and engagement. Mind wandering and disengagement can be detrimental to learning outcomes, making their automated detection via video-based indicators a promising approach for real-time learner support. However, machine learning-based approaches often require sharing sensitive data, raising privacy concerns. Federated learning offers a privacy-preserving alternative by enabling decentralized model training while also distributing computational load. We propose a framework exploiting cross-device federated learning to address different manifestations of behavioral and cognitive disengagement during remote learning, specifically behavioral disengagement, mind wandering, and boredom. We fit video-based cognitive disengagement detection models using facial expressions and gaze features. By adopting federated learning, we safeguard users' data privacy through privacy-by-design and introduce a novel solution with the potential for real-time learner support. We further address challenges posed by eyeglasses by incorporating related features, enhancing overall model performance. To validate the performance of our approach, we conduct extensive experiments on five datasets and benchmark multiple federated learning algorithms. Our results show great promise for privacy-preserving educational technologies promoting learner engagement.