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In contrast to the classical concept of a Carnot engine that alternates contact between heat baths of different temperatures, naturally occurring processes usually harvest energy from anisotropy, being exposed simultaneously to chemical and thermal fluctuations of different intensities. In these cases, the enabling mechanism responsible for transduction of energy is the presence of a non-equilibrium steady state (NESS). A suitable stochastic model for such a phenomenon is the Brownian gyrator -- a two-degree of freedom stochastically driven system that exchanges energy and heat with the environment. In this context, we exploit the relationship between optimal mass transport and stochastic thermodynamics to present a geometric view of the energy harvesting mechanism, that entails a forced periodic trajectory of the system state on the thermodynamic manifold. Dissipation and work output are expressed accordingly as path integrals of a controlled process, and fundamental limitations on power and efficiency are expressed in geometric terms via a relationship to an isoperimetric problem. The analysis presented provides guiding principles for building autonomous engines that extract work from anistropic fluctuations.