The integration of Augmented Reality (AR), Virtual Reality (VR), and Digital Twin (DT) technologies has shown significant promise in enhancing remote collaboration, enabling synchronization between virtual and physical assets. In complex smart home environments, identifying faults in physical systems and finding service providers with the precise skills remotely required for maintenance is a significant challenge. Current remote services rely on traditional communication methods, such as video calls, which provide limited interaction between remote service providers and physical machines where maintenance problems are located. The Metaverse could bridge this gap by linking virtual and physical spaces using DTs to improve task assignment and the remote service process. In this paper, we present a framework for Metaverse-oriented remote servicing based on DT that maps fault identification to task allocation. Identified faults serve as the basis for the task assignment optimization model, which aims to improve skill matching between service providers and DTs for people-digital twin task allocation within the remote service for smart homes. The proposed approach considers multi-objective factors by extending the Hungarian algorithm to accommodate task scheduling for dynamic DT task allocation. We evaluated the potential of our approach using remote home maintenance in a use case of Heating, Ventilation, and Air conditioning (HVAC) systems. We show that integrating DT improves the skill relevance of the assigned service providers by 27.5% and the reputation of the service providers by 8.4% compared to two baseline methods.