I would like to ask about what are the pathways of the illah (legal cause/ratio legis)?

This topic requires a separate study, and a comprehensive answer cannot be provided in a brief fatwa. Therefore, we advise referring to the following sources: "Al-Bahr Al-Muhit" by Al-Zarkashi, "Al-Mustasfa" by Al-Ghazali, "Jam' Al-Jawami'" by Al-Subki, "Al-Fusul fi Al-Usul" by Al-Jassas, "Kashf Al-Asrar" by Abd Al-Aziz Al-Bukhari, "Al-Tawdih" by Al-Taftazani, "Tabsira Al-Hukkam" by Ibn Farhun, "Al-Taqrir wa Al-Tahbir" by Ibn Amir Al-Hajj, "Al-Insaf" by Al-Mardawi, and "Sharh Al-Kawkab Al-Munir" by Al-Futouhi.