Recycling and the use of secondary aluminum represent a promising route toward climate-neutral aluminum production due to their substantially reduced energy consumption and emissions compared to primary aluminum. However, secondary alloys commonly suffer from increased iron contamination introduced during processing and recycling, which promotes the formation of needle-like, brittle Fe-containing intermetallic phases (IPs), thereby deteriorating mechanical properties such as yield strength, ultimate tensile strength, and strain to failure. In this work, we present a computational- and data-driven framework for microstructure optimization of high-quality secondary aluminum alloys, demonstrated using the prototype system AlSi10MnMg under a fixed and elevated Fe content of 0.8%. Alloy microstructures with systematically varied intermetallic phase characteristics are generated and quantitatively represented using descriptors such as orientation, aspect ratio, size, and inter-particle spacing, including their statistical means and standard deviations. Cohesive phase-field fracture simulations are conducted on experimentally derived (like SEM), digitized and meshed microstructures to quantitatively predict mechanical responses, including ultimate tensile strength and strain to failure, as well as to resolve fracture patterns such as brittle cracking within IPs and ductile fracture in the matrix, and interfacial decohesion between phases, thereby enabling rigorous physical model validation. Building upon those, high-throughput finite element simulations are employed to systematically evaluate the influence of microstructural descriptors on mechanical performance. A Bayesian-optimization-based inverse design strategy is then applied to efficiently navigate the high-dimensional descriptor space and iteratively propose optimal microstructural configurations that maximize targeted mechanical properties. This study provides quantitative, physics-informed design guidelines for enhancing the mechanical performance of secondary aluminum alloys through targeted microstructural tailoring.