This really isn't a genre I'm a fan of, but uhh.... ummm.... huh. I have one in mind that's a DS game that was kind of cool, but it's a huge spoiler to reveal it. Also it ended up tossing away the mystery as the story progresses which I think was kind of a mistake, but it was kind of cool how it happened I guess.
If you'll never play a sci-fi DS game I can tell you what it is I guess: Infinite Space.
It's also a really cool general sci-fi game, although it gets kind of tedious if you don't like the gameplay. I didn't like it, but I powered through because of the awesome story. People compared it to something like LoGH since it's a big space opera thing. Anyway, the TRUE SPOILER DO NOT READ ANY FURTHER IF YOU'RE MAYBE GOING TO PLAY ONE DAY: The protag goes on a typical sci-fi adventure but weird stuff starts happening and protag's recollection of events doesn't match with previous facts. I can't remember what, but they end up searching for something. There is some girl, I think it was his love interest, but I can't remember. She starts using some artifact thing to probe, uhh... something about reality and starts to bypass restrictions as warnings go off. Anyway, a REALLY creepy and well done moment happens when this regular girl is instantly turned into an empty robot shell like a marionette as a brief glimpse of skinny alien silhouettes look down. Her entire existence was erased as no one but the protag remembers her ever existing. It was an extremely well done "you are messing with powers you shouldn't" moment.
It turns out the entire universe was a microscopic creation of a higher dimensional race. The protag had a special role in that he determined the effects of quantum events of this micro universe by observing them and that's why reality seemed to shift around him. The micro universe was used to generate energy and the creators unleash weird biological warships that bypass physics as the universe gets chipped away and harvested/deleted. I don't know if this counts as cosmic horror stuff.
Maybe that's not horror, but it's the closest thing I know apart from Saya since it's not stuff I go looking for. Man, it was such a cool story. I believe the studio that made it is gone, sadly.

All I can offer is nothing. From the Neverending Story. I remember it as the first time I felt a sort of dread. Though it might seem like a cheeky trick, to give a threat infinite scale by having it be nothing. To have it be utterly unreasonable by having it be nothing. Nothing to face, nothing to imagine, indeed nothing to comprehend, just by being nothing.

The other anon already mentioned Saya no Uta, so I'll mention Otonashi Ayana from Subahibi. She gives off an otherwordly incomprehensible vibe that you may just be looking for. Some of the scenes with her really creep me out.
>>124109
Gonna check this game out, thanks.

It's interesting that Madome uses maou (translated as archdemon) to refer to a high-ranking sorcerer (majutsushi) rather than an actual demon or even a commander (>>122123), and for the summoned entity they use mazoku which typically means demons as a race (zoku/族 is for groups and has more of a familial connotation), then when talking about the "gods and devils" that gave humanity the ability to use magic they say kami and akuma. The "ma" in all of these words is the same 魔. It's hard to tell at what scale the akuma operates since its shadow appeared for such a short time, but if it's a truly celestial thing then those are more commonly straight up referred to as dark gods or something like that rather than simply a demon.
I haven't seen or read Dorohedoro, but I understand that its demons are pretty fucked up and well above everyone else. Featherine is one example of an entity that operates on a higher level of existence, and to a lesser degree you have any character that's mindblowingly powerful like this silly autistic shota that ranges from having his horrified foes saying he's literally stronger than God (not yet proven afaik) to being hugged by his friends like a regular child.

>>124121
What a freaking looking character. Do deformed chibi things count as eldritch? I think they should.

>>124161
I JUST BIT THIS SHAB

>>124161
Eldritch ween.

>>124107
From Touhou, when Yukari isn't being a complete dork and jobs to villain of the month, she exhibits this perfectly. Her power of manipulating boundaries is purposefully vague and is only as powerful as the author wants it to be. Canon doesn't explore this very often since they're just not Yukari centric and her Gaps are mainly just useful plot devices, in fanon on the otherhand, some works explore this to the extremes. From simply pulling lovecraftian horrors out of a hat, to changing the way the world works around you, shattering common sense and logic, and playing with boundary of right and wrong or real and imaginary.

>>124161
It kinda reminds me of the funny faces in western web animations. Wonder if they actually were able to cross overseas and have influence over in Japan since Niconico lost popularity.

>>124169
It's not western corruption, it's a guy using proportions derpier than usual predominantly for contrast. Here the chibi looks all normal, but >>124121 is him being menacing.