There is a Cthulhu connection in TOS - Robert Bloch, who wrote multiple Cthulhu mythos stories, wrote three TOS episodes, “What Are Little Girls Made Of?”, “Catspaw” and “Wolf in the Fold.” And there are refernces to “The Old Ones” in the first two of those. And as Redjac from Wolf in the Fold has some definite horror elements (as you say above C57D).
Ultimately though, I don’t think we see many Cthulhu-ish elements because an essential aspect of Cthulhu mythos tales is helplessness in the face of cosmic horror - and that doesn’t mesh so well with the generally utopian, triumph of the human spirit feel of Star Trek. Similarly, most Cthulhoid entities have unknowable, alien motives, and normally pay little or no attention to mortals, which doesn’t make for great Trek adversaries.