Microarchitected structures enable superior performance and therefore reduce material usage. However, the necessary multiscale simulations are prohibitively expensive for practical application, particularly when embedded within optimization frameworks. Data-driven surrogates for the microscale can accelerate these simulations, but face challenges regarding large dataset requirements, extrapolation, and microstructural variations. In this work, we show the potential of hybrid physics-data surrogates conditioned on microstructure descriptors to overcome these challenges. We demonstrate this approach by performing a multiscale optimization on an engineered living material for large deformations. Microscale geometric and material properties of a fungi-woodchip composite are varied throughout the domain to optimize for macroscale performance. A hypernetwork learns to condition the surrogate on the microscale variables, enabling accurate predictions of microstructural responses across a broad range of microstructures. We show that this approach yields fast and accurate simulations for functionally graded multiscale materials. This enables Bayesian optimization of the multiscale structure, finding the optimal microstructural grading that maximizes structural performance under weight constraints. More broadly, this contribution highlights the benefits of microarchitectured structures and demonstrates how machine-learning-based surrogates enable their multiscale optimization.