Large-scale Internet of Vehicles (IoV) deployments increasingly demand the on-device adaptation of foundation models to support diverse, mission-critical perception tasks. While federated fine-tuning offers a promising solution for efficient model specialization, existing approaches often struggle to reconcile the inherent conflict between stringent global energy budgets, heterogeneous task demands, and the high volatility of vehicular network connectivity. In this work, we introduce a hierarchical, adaptive framework that decouples multi-task fine-tuning into two interdependent optimization phases. First, we implement a feedback-loop mechanism at the infrastructure level that dynamically redistributes global energy budgets across concurrent tasks based on real-time convergence dynamics and resource utilization. Second, at the vehicle level, we formulate intra-task rank selection as an energy-constrained online learning problem, solved via a novel primal-dual bandit algorithm, UCB-DUAL, which provides theoretical guarantees on sublinear regret. Our approach effectively internalizes global energy constraints into local decision-making, allowing vehicles to autonomously navigate the complex trade-off between model accuracy, latency, and power consumption. Empirical evaluations using a large-scale IoV simulator, driven by real-world trajectory data, confirm that our proposed method significantly outperforms current federated fine-tuning baselines, offering a robust and scalable solution for resource-constrained vehicular intelligence.