We'll probably never get any confirmation of this but I'm pretty sure Braun was at least inspired from Nyarlathotep if he isn't actually the Outer God himself. Hear me out on this lol.
I discussed this a couple of times with some of my mutuals when I thought of it but I feel like I should probably at least put it all into coherent sentences.
Right of the bat in the novel when we're introduced to Braun, we're told that he's merely a D-Grade Darkness but as it soon becomes clearly evident, that is not even nearly the case at all. While the Tuesday Night Talk Show may have been D-Grade due to its low lethality nature, we see that such is not the case for its Host.
Despite the Smiley Stickers doused in the enhancement potion, Braun is fully aware of Soleum trying to trick him into delaying a bit in order for their survival and he's not even mad about it, he finds Soleum all the more fascinating for it. Which, of course, we learn the reason for afterwards... cough 208 cough but that's not it.
During his first invitation into the Good Friend rabbit plushie, we hear a massive roar of titles and Soleum gets shit scared before it all shuts up so we can finally talk with our favorite show host. I'll just put the titles announced below:
"...the owner of a million masks, the lord of chaos, the pinnacle of madness, the dreamer of pleasure and play, the instigator of war, the father of science, the lowly quadruped, the desire of the one who dreams, the monarch of the stars, the abyss of illusion, the mouth of wisdom, the roar of impulse, the dark side of the moon..."
Sound familiar? This was the moment I first actually thought of this theory, once I actually processed all these titles. Of course, some of these are obvious signs of Braun being an Outer God/Eldritch Horror but what about some of the other weird ones? Why is an entertainer being called "the father of science"???
It's because he isn't an entertainer. 'Braun' is merely a disguise.
But entertainment and allure is definitely one of his aspects.
It'll make sense in a moment.
Because if you now take a quick trip to Lovecraft and the cosmic horror town and look at some of Nyarlathotep's innumerable titles, you'll find these:
Crawling Chaos
God of a Thousand Forms
Stalker Among The Stars
Black Pharaoh
Faceless God
Messenger & Soul Of The Outer Gods
Just read it over a couple times and you're bound to see the obvious similarities between the titles of the two characters. As for the last title of Nyarlathotep, he's Azathoth's servant/messenger/lieutenant.
Now for the father of science part, just take a look at this:
"I had never heard the name NYARLATHOTEP before, but seemed to understand the allusion. Nyarlathotep was a kind of itinerant showman or lecturer who held forth in public halls and aroused widespread fear and discussion with his exhibitions. These exhibitions consisted of two parts—first, a horrible—possibly prophetic—cinema reel; and later some extraordinary experiments with scientific and electrical apparatus."
"...But Loveman's dream letter decided me.... As I left the house I saw throngs of men plodding through the night, all whispering affrightedly and bound in one direction. I fell in with them, afraid yet eager to see and hear the great, the obscure, the unutterable Nyarlathotep."
Pretty on the nose right? He's an expression of allure and what is more alluring to thousands if not entertainment? Everyone loves it. Moreover, he's maddening convincing, a true showman despite the terror he invokes from people.
A couple of things to be noted about Nyarlathotep is that he's the ONLY Outer God who's capable of interacting normally with people. He's not trapped anywhere either, he's free. You could meet him at a cafe and exchange a smile and nod and get away with it. At the same time however, he could destroy just about everything with his will. The best analogy I can find for this is a kid at an anthill with some sugar and a magnifying glass.
Another thing I noticed was Braun's disdain towards the 'producers' of his show. The first time in the novel he shows open hostility in his face is when he's talking about the execs who 'cancelled' his show, saying that they "knew nothing" about show business and what they're doing.
And after Part 2 I can be sure about one thing, he was very clearly talking about Ireum-nim. He does a couple of similar fourth wall breaks later too.
To put it in terms, Nyarlathotep's the servant of Azathoth, his father. However, he despises Azathoth going so far as to give him the title of "The Blind Idiot God." And that's because Azathoth is literally that, a dumbass to him. As per later renditions, all of existence including Nyarlathotep himself exists within Azathoth's dream and to wake Azathoth would mean the ceasing of everything. But Azathoth himself does not interact nor know anything and yet all is at his whim.
I'd be frustrated as fuck too. Braun's this immensely powerful guy but he's not exactly at the top, he's subject to the whims of incompetent superiors (the writers; Ireum-nim) that he cannot affect in any significant way and so he does the most he can do with what he has.
That's where 'Braun' comes in imo, much like what one of his titles say, the entire persona of Braun is merely one of the millions of masks he wears, one of his thousand forms he takes up to achieve whatever unknown objective he has.
Or more likely, just another whim he has out of mere curiosity. Much like a kid at an anthill, he doesn't really have any reason to burn up the ants or destroy an anthill, he just does it because it's fascinating.
hastur, nyarlathotep and cthulhu in a "fuck humanity" meeting and shub-niggurath is there too but... she misunderstood the "fuck" part and now they are in a rather awkward situation