New Urbanization and Low-Carbon Energy Transition in China: Coupling Coordination, Spatial–Temporal Differentiation, and Spatial Effects

New urbanization (NU) and low-carbon energy transition (LCET) are important issues of Chinese-style modernization, with the necessity and possibility of coordinated development. By using panel data for 30 provinces from 2013 to 2022, this paper adopted the entropy method, principal component analysis, and coupled coordination model to evaluate the coupled coordination degree (CCD) of NU and LCET, and applied the Dagum Gini coefficient, kernel density estimation, and spatial Durbin model to reveal the regional differences and spatial effects of coupled coordination. Research found that the comprehensive levels of NU and LCET exhibit growing trends, with regional variations. The overall coupling coordination index steadily increased, accompanied by polarization. The intra-regional disparities are biggest in the west and smallest in the central region, while the inter-regional differences (except the central and northeast) show narrowing trends. The coupling coordination level shows a positive spillover effect. As for influencing factors, the levels of economic development, social consumption, energy consumption, and R&D intensity have an inhibitory effect on neighboring regions, while digital economy and environmental regulation intensity have a positive spatial spillover effect on neighboring provinces. Finally, countermeasures are proposed to promote the coordinated development of the two systems.