This study proposes a physics-informed machine learning framework for aerodynamic performance-driven shape optimization. While recent PINN-based approaches embed design variables into the solver and perform trajectory-based optimization toward a single optimal design, and DeepONet-based surrogate pipelines in engineering treat modeling and optimization as two decoupled stages, the proposed framework establishes a unified design paradigm in which the learning model itself functions as a reusable design engine over a family of geometries. To this end, a physics-informed DeepONet is developed to approximate the parametric flow operator under varying geometric configurations, enabling direct prediction of velocity and pressure fields without repeated CFD simulations. Aerodynamic performance metrics, including lift and drag coefficients, are computed from the predicted flow fields and incorporated into a differentiable optimization loop. This end-to-end formulation allows shape parameters to be iteratively updated toward prescribed performance objectives within a single computational graph. In contrast to traditional surrogate-based optimization, which learns uniformly over the design space, the proposed framework adaptively concentrates learning in performance-critical regions through iterative surrogate refinement and Bayesian design space contraction. This closed-loop learning strategy improves design reliability near target performance regimes while maintaining physical consistency across the broader parameter domain. By transforming the surrogate from a passive solver into an active design engine, the proposed method enables efficient exploration of high-dimensional design spaces under complex aerodynamic objectives. The framework provides a scalable and generalizable alternative to existing physics-informed and data-driven aerodynamic design methodologies.