I keep writing reviews that include a line to the effect that “it’s like Lovecraft, but it also explores aspects of human psychology that Lovecraft always ignored.” This has happened with The Ballad of Black Tom, Annihilation (the book and the movie), Prey, and The Friendship of Mortals. I’ve been writing this so much that I can’t call this an exception to the rule anymore. It has become a style of its own.
It feels wrong to call it “Lovecraftian” horror. Lovecraft deliberately minimized the role of human emotions and thoughts in all his stories. Lovecraft’s philosophy was that human beings were unimportant “incidents” in the grand cosmic scheme, and he wrote accordingly. That was part of the horror. (Hence “cosmic horror” as a synonym for “Lovecraftian”.)
The works I listed above certainly retain elements of cosmic horror, but flesh out their human characters, making them interesting and relatable. Whereas Lovecraft approached the horror of humanity’s place in the cosmos with a detached, dispassionate tone, subsequent writers have framed it by humanizing their characters first, then pitting them against the unimaginable outside forces.
This style is also different from the kind of horror that humanizes things too much to be called “cosmic”. Stephen King, for example, writes in a style more like that of noir detective thrillers that feels too immediate and gritty to be “cosmic”—even in stories that have what you might call Lovecraftian elements. (e.g. 11/22/63) The works I’ve described above are much closer to a 50/50 balance than King’s style of an “earthly” horror story with a few cosmic elements.
My point isn’t that any one of these styles is better or worse than the others; but just to point out that they are distinct, and that I don’t know of any term that fits stories like those I’ve listed here. Calling them “semi-Lovecraftian” or “semi-cosmic” feels too weak. “Weird fiction” or “New Weird fiction” is too broad. The best I can come up with is “humanized cosmicism”, but that sounds awkward.