Currently (Requiem+Pandemonium 1.5.0 and Minecraft 1.16.4), when you are near an Elder Guardian and not in human form, some unexpected things happen regarding the Mining Fatigue effect:

1. Base case (human form): You are inflicted with Mining Fatigue III, as intended.
2. Possessing any entity: The entity you are possessing is inflicted with Mining Fatigue III, as shown when you leave the entity.
3. In soul form: You are still inflicted with Mining Fatigue III, but that does not immediately carry over to entities that you possess.

What I would expect:

1. Base case (human form): You are inflicted with Mining Fatigue III, as intended.
2. Possessing any entity: As Elder Guardians don't usually inflict non-player entities with Mining Fatigue, you shouldn't get Mining Fatigue just by being near an Elder Guardian if you are not in human form.
3. In soul form: Same as case 2 (no Mining Fatigue from being near an Elder Guardian).

I think it's fair to apply fatigue to possessed mobs.
It's probably safe to assume that the only reason fatigue isn't applied to vanilla mobs is that they can't break blocks (most can't at all, none can do it by attacking blocks like players do).

Not sure what we want to do with that one. I think n°2 is going to stay at least.