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While the literature on RF fingerprinting-based authentication and key distillation is vast, the two topics have customarily been studied separately. In this paper, starting from the observation that the wireless channel is a composite, deterministic / stochastic process, we propose a power domain decomposition that allows performing the two tasks simultaneously. We devise intelligent pre-processing schemes to decompose channel state information (CSI) observation vectors into "predictable" and "unpredictable" components. The former, primarily due to large-scale fading, can be used for node authentication through RF fingerprinting. The latter, primarily due to small-scale fading, could be used for semantically secure secret key generation (SKG). To perform the decomposition, we propose: (i) a fingerprint "separability" criterion, expressed through the maximisation of the total variation distance between the empirical fingerprint measures; (ii) a statistical independence metric for observations collected at different users, expressed through a normalised version of the $d$-dimensional Hilbert Schmidt independence criterion (dHSIC) test statistic. We propose both explicit implementations, using principal component analysis (PCA) and kernel PCA and black-box, unsupervised learning, using autoencoders. Our experiments on synthetic and real CSI datasets showcase that the incorporation of RF fingerprinting and SKG, with explicit security guarantees, is tangible in future generations of wireless.