A full-scale finite element model is presented for monolithic fluid-structure interaction (FSI) simulations of thin-walled piezoelectric fluid energy harvesters (PFEH). Unlike widely used beam/plate-based models, our model employs a solid finite element discretization to precise represent the complex PFEH designs involving microstructured transducers and non-uniform cantilevers. These features, plus the local FSI effects, are often ignored by simplified models. We applied the Galerkin method to formulate the weak form of the mixed equation system, integrating the flow dynamics, the geometrically nonlinear cantilever, the piezoelectric components, the electrode, and the output circuit within a closedcircuit electro-mechanical coupled system. The coupling of the multiple domains is achieved through boundary-fitted discretization within a monolithic scheme, using shifted-Crank-Nicolson temporal integration. This work explored implementing piezoelectric FSI systems within the FEniCS-based TurtleFSI library, and experimented techniques such as employing penalty functions for achieving electrode components with uniform electric potentials. We investigated various advanced PFEH features, including the base plate design, the arrangement and microstructure of the piezoelectric components, and their influence on the system's dynamic and energy output behavior. The results confirmed the model's effectiveness and potential to assist the design and optimization of PFEH systems.