Time to get down to this
What we need to truly look at is what toby fox intended annoying dog in the actual game itself to be. Him portraying annoying dog as one thing outside of the game does not affect what he is inside the game.
For example, if i created an avatar of myself called postman who is a literal representation of myself that i posted about on paper, and then i programmed it into a game which for this instance is canonically a game as well. However postmans feats ingame is just doing nothing but delivering letters and in his spare time, creating video games which resemble the game i created. Whilst the character idea of postman in general is a literal representation of me, ingame I would have only programmed him to be a random npc who makes gag references to me and through my own intent, isnt some supreme being nor creator.
This is why you cant take information about a character outside its own series. Otherwise you are not focusing on what the character is supposed to be in that specific game and just focusing on the character idea in general which is just blatantly going against cannon material.
Anyway, the annoying dog only has the following feats
- Creating a game which resembles undertale
- Needing to patch holes in the fabric to fight the dog
- Him talking about hardmode
- Appearing in certain places and even being able to teleport in frisks inventory and in a neutral ending
- Existing after a game crash
Patching the holes
This is status effect inducement, and to some extent reality warping, physics manipulation and data manipulation. He is able to fix patches supposedly in reality and stop you from fighting him until he does so. Ap wise this is unquantifiable as the scale he is doing this is unknown.
==Creating a game==
Nothing noteable as it doesnt scale to the reality itself
==Appearing in many places==
Being able to appear in multiple places individually does not give you omnipresence. At best this is just teleportation.
Appearing in hard mode
Here we see that annoying dog has some influence on the game as he created the game mode where he made all of the enemies tougher. There are two possibilities as to where this falls under authors intent. First being that annoying dog was just making everyone stronger and was messing around with the game a little bit (but not on some multiversal scale). Or that annoying dog was actually the creator of the game and is a legitimate developer that is adding an incomplete section of the game (which if finished would involve a possible amp for asriel in his fight as well).
Considering how the other characters are heavily implied to view him as the developer in that scene, and he is able to give everyone 4th wall awareness, it is more likely he was the game developer in that scene and is the creator and programmer of undertale.
However due to this not heavily being enforced anywhere else, it is safer to give him an unknown, possibly 2-B rating as the other scenario is still possible.