Unmanned Aerial Vehicle (UAV) Coverage Path Planning (CPP) is critical for applications such as precision agriculture and search and rescue. While traditional methods rely on discrete grid-based representations, real-world UAV operations require power-efficient continuous motion planning. We formulate the UAV CPP problem in a continuous environment, minimizing power consumption while ensuring complete coverage. Our approach models the environment with variable-size axis-aligned rectangles and UAV motion with curvature-constrained Bézier curves. We train a reinforcement learning agent using an action-mapping-based Soft Actor-Critic (AM-SAC) algorithm employing a self-adaptive curriculum. Experiments on both procedurally generated and hand-crafted scenarios demonstrate the effectiveness of our method in learning energy-efficient coverage strategies.