As artificial intelligence (AI) evolves from an augmentation technology to a shared infrastructure for enterprise payment systems, financial services are increasingly adopting stateful, agent-based architectures that maintain transaction context and execution state throughout continuous payment workflows. This study examines the architectural integration of AI agents, managed cloud infrastructures, standardized interfaces, and human oversight within enterprise financial operations. The approach analyzes how agentic architectures support interconnected processes, including credit decisioning, fraud detection, checkout personalization, invoice processing, and multi-entity reconciliation, while maintaining reliability, observability, identity boundaries, and operational control. Particular attention is given to standardized interfaces that enable memory management, tool invocation, and identity-bounded execution, as well as to human-in-the-loop mechanisms for decisions requiring explanation, compliance review, or exception handling. The analysis shows that stateful agent-based infrastructures can reduce dependence on external orchestration by enabling agents to coordinate multi-step workflows and retain relevant operational context. AI-supported classification and natural language processing can further automate post-transaction activities such as e-invoicing and reconciliation. At the same time, human-based exception management remains necessary for ambiguous transactions, regulatory uncertainty, and atypical cases. Bidirectional learning also enables human corrections to refine model behavior while AI-generated patterns support human understanding of financial processes. The findings indicate that agentic architectures can extend enterprise payment platforms beyond isolated automation toward continuously coordinated financial operations. Their effective deployment, however, depends on combining autonomous execution with explicit human oversight, traceability, compliance controls, and reliable monitoring. The resulting architecture represents a convergence of intelligent automation and human governance in the development of next-generation enterprise financial platforms