Sustainability reporting for web-based services often relies on simplified end-user energy models that assume constant laptop power during browser interactions. Energy models such as Digst and DIMPACT apply fixed power values (15-22W), yet the validity of this approach for realistic browsing remains underexplored. We empirically evaluate constant-power assumptions in a controlled user study where ten participants repeatedly complete eight representative user flows across shopping, booking, navigation, and news services on four laptop platforms, while device energy is measured. Typical power is 9--13~W, substantially below current reporting standards, implying systematic overestimation. Moreover, the error scales proportionally with task duration, indicating systematic bias rather than random noise. Comparing progressively refined constant-power models, we find that category-specific parameters improve accuracy more than hardware-only parameters and approach flow-specific performance. The best fit is obtained by combining category (or flow) with hardware, while category-level models retain most of the benefit with fewer parameters, making them a practical upgrade for sustainability reporting.