This article explores the transformative potential of Large Language Models (LLMs) in enhancing cloud-native observability and accelerating application modernization in Platform as a Service environments. Traditional observability tools struggle to provide actionable insights in cloud-native systems due to the complexity of microservice-based architectures. By integrating LLMs with traditional observability toolchains, organizations can overcome the limitations of conventional approaches to gain deeper insights into distributed systems. Through a detailed case study in the financial services sector, the article demonstrates how AI-driven observability facilitates more effective anomaly detection, improves mean time to resolution(MTTR), and supports application modernization through intelligent code refactoring. The mixed-methods evaluation reveals significant improvements across multiple dimensions, including system reliability, resource utilization, and customer satisfaction. Despite implementation challenges related to technical integration, privacy concerns, and organizational resistance, the economic benefits of LLM-enhanced observability are substantial. The article concludes by outlining future directions, including multimodal observability, federated learning approaches, self-healing systems, and ethical frameworks for increasing automation in critical infrastructure.