The rapid transition of ICT towards AI-native operation is fundamentally reshaping the sustainability landscape of future 6G systems. While AI has long been seen as an enabler of decarbonisation through digitalisation, the proliferation of large-scale AI workloads, distributed training, and inference services now poses significant challenges in terms of energy consumption and carbon footprint. This joint talk brings together complementary perspectives from the EXIGENCE and NATWORK projects to address these challenges through coordinated, system-level approaches to sustainable operation. The contribution explores how green orchestration can align AI workload placement, partitioning, and execution with real-time energy conditions, network capabilities, and service constraints, enabling adaptive and carbon-aware operation across training and inference phases. Building on this, incentive mechanisms are introduced as AI-native tools to align individual user and stakeholder decisions with system-wide sustainability objectives, balancing performance, quality of experience, and environmental impact. At the system level, the talk highlights the need for federated orchestration across autonomous domains and stakeholders, enabling sustainable service delivery through interoperable data exchange, adaptive coordination, and cross-domain decision making. By combining green orchestration, incentive-driven optimisation, and federated coordination mechanisms, the joint contribution illustrates how AI-native 6G systems can move towards truly operationally sustainable architectures that scale across heterogeneous infrastructures and organisational boundaries. Presentation done at EuCNC & 6G Summit 2026 - Workshop 11: "Sustainable by Design, Sustainable in Operation: The 6G Perspective"