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Massive multiple-input multiple-output (mMIMO) downlink precoding offers high spectral efficiency but remains challenging to deploy in practice because near-optimal algorithms such as the weighted minimum mean squared error (WMMSE) are computationally expensive, and sensitive to SNR and channel-estimation quality, while existing deep learning (DL)-based solutions often lack robustness and require retraining for each deployment site. This paper proposes a plug-and-play precoder (PaPP), a DL framework with a backbone that can be trained for either fully digital (FDP) or hybrid beamforming (HBF) precoding and reused across sites, transmit-power levels, and with varying amounts of channel estimation error, avoiding the need to train a new model from scratch at each deployment. PaPP combines a high-capacity teacher and a compact student with a self-supervised loss that balances teacher imitation and normalized sum-rate, trained using meta-learning domain-generalization and transmit-power-aware input normalization. Numerical results on ray-tracing data from three unseen sites show that the PaPP FDP and HBF models both outperform conventional and deep learning baselines, after fine-tuning with a small set of local unlabeled samples. Across both architectures, PaPP achieves more than 21$\times$ reduction in modeled computation energy and maintains good performance under channel-estimation errors, making it a practical solution for energy-efficient mMIMO precoding.