Distribution of ΔPA, the position–angle difference between the radio axis (PA_radio: jet direction) and the optical major axis (PA_optical) of the host galaxy for GRGs. The ΔPA distribution indicates that a small fraction of GRG sources deviate from the expected alignment trends with the host’s principal axis (Sect. 3), highlighting the presence of counterexamples (e.g., sources with ΔPA ≲ 45°).