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We present a theoretical study of topological superconductivity in proximitized planar Josephson junctions (JJs), demonstrating how structural and magnetic mirror symmetries enable distinct topological classes hosting multiple Majorana states whose localization character can be tuned from end-like to edge-like by varying the superconducting phase difference across the junction. We further show that the magnetocurrent–phase relation (magneto-CPR) provides direct signatures of topological gap closings, enables reconstruction of the topological phase diagram, and allows experimental estimation of key parameters such as the Rashba spin–orbit coupling (SOC) strength. The magneto-CPR also reveals the behavior of the Josephson diode effect (JDE) and its dependence on SOC, Zeeman field, and junction transparency. A symmetry analysis identifies magnetic-field and crystallographic orientations for which the JDE is suppressed, offering experimentally testable signatures of the interplay between Rashba and Dresselhaus SOCs, and Zeeman coupling. In addition, numerical simulations show that electrostatic gating can induce polarity reversals of the JDE in the low-field regime even in the presence of only Rashba SOC, consistent with recent experiments, and predict further reversals for specific field orientations, junction geometries, and SOC ratios. These results establish magneto-CPR measurements as a versatile probe of topological superconductivity and nonreciprocal transport in semiconductor-based planar JJs.