We present VEGA, a vehicle-adaptive energy-aware routing system for electric vehicles (EVs) that integrates physics-informed parameter estimation with RL-based charge-aware path planning. VEGA consists of two copupled modules: (1) a physics-informed neural operator (PINO) that estimates vehicle-specific physical parameters-drag, rolling resistance, mass, motor and regenerative-braking efficiencies, and auxiliary load-from short windows of onboard speed and acceleration data; (2) a Proximal Policy Optimization (PPO) agent that navigates a charger-annotated road graph, jointly selecting routes and charging stops under state-of-charge constraints. The agent is initialized via behavior cloning from an A* teacher and fine-tuned with cirriculum-guided PPO on the full U.S. highway network with Tesla Supercharger locations. On a cross-country San Francisco-to-New York route (~4,860km), VEGA produces a feasible 20-stop plan with 56.12h total trip time and minimum SoC 11.41%. Against the controlled Energy-aware A* baseline, the distance and driving-time gaps are small (-8.49km and +0.37h), while inference is >20x faster. The learned policy generalizes without retraining to road networks in France and Japan.