Radio frequency (RF) wireless energy transfer (WET) is a promising technology for powering the growing ecosystem of Internet of Things (IoT) using power beacons (PBs). Recent research focuses on efficient PB architectures that can support numerous antennas. In this context, PBs equipped with intelligent surfaces present a promising approach, enabling physically large, reconfigurable arrays. Motivated by these advantages, this work aims to minimize the power consumption of a PB equipped with a passive intelligent transmitting surface (ITS) and a collocated digital beamforming-based feeder to charge multiple single-antenna devices. To model the PB's power consumption accurately, we consider power amplifiers nonlinearities, ITS control power, and feeder-to-ITS air interface losses. The resulting optimization problem is highly nonlinear and nonconvex due to the high-power amplifier (HPA), the received power constraints at the devices, and the unit-modulus constraint imposed by the phase shifter configuration of the ITS. To tackle this issue, we apply successive convex approximation (SCA) to iteratively solve convex subproblems that jointly optimize the digital precoder and phase configuration. Given SCA's sensitivity to initialization, we propose an algorithm that ensures initialization feasibility while balancing convergence speed and solution quality. We compare the proposed ITS-equipped PB's power consumption against benchmark architectures featuring digital and hybrid analog-digital beamforming. Results demonstrate that the proposed architecture efficiently scales with the number of RF chains and ITS elements. We also show that nonuniform ITS power distribution influences beamforming and can shift a device between near- and far-field regions, even with a constant aperture.