@Sailorsadie
Glad that you’re interested. Do you have any character concept in mind or at least what kind of monster you want to be?
@Havoccultist
Glad that you also have an interest in this. While I’m not super familiar with all the beings of the Cthulhu mythos, out of the three mentioned, I believe Nyarlathotep would probably work the best, or you could create an original eldritch being. The only problem with these kind of characters is that they exist on cosmic level and might not have any real stake in what is going on on Earth. But if you reworked Nyarlathotep a little bit, maybe toning down his powers, I could see him as a member of the Council of Night.
Given that at most what I know of Nyar consists of shapeshifting troll who uses magic to cause chaos, I don't think that should be too hard lol. Sure he is much greater than that power wise, but a toned down version like that should work well enough I think. I could also make a custom eldritch entity as you mentioned, which would be easier since I only really see it affecting things on a planetary level at most. Although even then that'd be through gradual influence and a kind of infectious madness as its influences spreads or it awakens, etc., rather than all at once.
I will note that Hastur is a strictly planetbound being as well from what I can tell, at least so far as his influence goes. Sure he spreads it via the Yellow Sign, but he is confined to Carcosa from what I know, and has been stuck there ever since he (possibly) landed on and corrupted it ages ago. I say possibly because like all things Mythos or Yog-Sothery related, it's left rather vague. For more info on him specifically, there's this: lovecraft.fandom.com/wiki/Hastur
Because of this he might work better, as I can play him more as an eldritch royalty type deal instead of a strictly cosmic entity.