Residential occupancy detection has become an enabling technology in today's urbanized world for various smart home applications, such as building automation, energy management, and improved security and comfort. Digitalization of the energy system provides smart meter data that can be used for occupancy detection in a non-intrusive manner without causing concerns regarding privacy and data security. In particular, deep learning techniques make it possible to infer occupancy from low-resolution smart meter data, such that the need for accurate occupancy detection with privacy preservation can be achieved. Our work is thus motivated to develop a privacy-aware and effective model for residential occupancy detection in contemporary living environments. Our model aims to leverage the advantages of both recurrent neural networks (RNNs), which are adept at capturing local temporal dependencies, and transformers, which are effective at handling global temporal dependencies. Our designed hybrid transformer-RNN model detects residential occupancy using hourly smart meter data, achieving an accuracy of nearly 92\% across households with diverse profiles. We validate the effectiveness of our method using a publicly accessible dataset and demonstrate its performance by comparing it with state-of-the-art models, including attention-based occupancy detection methods.