The rapid change in data needs in hybrid computing environments requires smart and flexible database schema management. This paper presents Neuro-Schema Adaptation (NSA), a new framework driven by AI. It uses machine learning and neural networks to automate schema evolution, matching, and optimization across different database systems. NSA tackles key challenges in modern data management, such as schema drift, compatibility problems, and migration difficulties in hybrid cloud-edge environments. Through detailed analysis of recent progress in AI-powered schema management, this research shows how neural methods can greatly improve schema adaptation efficiency, lessen manual work, and keep data safe during changes. The framework includes large language models, graph neural networks, and retrieval-augmented matching techniques to create a self-adjusting schema management system. This system can handle complex data changes in real-time.