Do effects that interact with “gaining” Power Cards apply to every time a Spirit gets a new Power Card, no matter the method?

Do effects that interact with “gaining” Power Cards apply to every time a Spirit gets a new Power Card, no matter the method?

No, only if the Spirit explicitly “gains” that Power Card (usually by drawing four cards and picking one to keep). If they “take” a Power Card, are given a Power Card, or otherwise receive a Power Card without being told to “gain” it, then they have not “gained” a Power Card.