I think this is where Savage Worlds got things right. They decoupled "powers" (termed Trappings) from their source, so that you can add in a new way of doing things without having to come up with a whole new subsystem. Invisibility has the same mechanical effects, whether it is granted by Faith, a Demon Pact, Psionics, Superpowers, Mad Science or some flavor of Arcane Magic.
D&D 5E almost did it right, but started with the premise that all this stuff is a magical spell, rather than leaving it open to being from a Martial, Supernatural, Divine, Pact, etc. source where the mechanics would be the same but might be from a different source - and that source could have have its own distinct methods and/or "Trappings" (such as bargain rules for Pacts, faith and devotion rules for Divine, study & prep mechanics for Wizardly Arcane, blood power points for Sorcery, focus & meditation rules for Psionics, training for Martial, etc.)