preventing down syndrome is "eugenics"?

Technically no, but only in the technical sense that makes the idea a little useless.

Technically, 99% of Down's cases aren't hereditary (it's a spontaneous mitotic change), so you don't "improve the gene pool" by excluding it; as far as we know, basically anybody can have a kid with Down's syndrome if the mitotic dice come up snake eyes.

(But in the sense most people understand the term? Yes.)

Yes, modifying genetics to select for "desirable" traits and remove "undesirable" ones is essentially modern liberal eugenics.

Just because something is labeled "eugenics" doesn’t automatically make it bad or good—outcomes depend on how ideas are applied.

Historically, eugenics didn’t have genetic tools, so efforts focused on social policies, like promoting abortion or family planning, to influence who could reproduce.

Seems close enough to look like it if you squint a little. As it's more of a genetic error than an inerited trait, maybe not quite the same.

Genetic conditions are how they make it palatable, meanwhile they're telling race realist parents that selecting for/modifying X, Y, and Z genes will let them raise ubermensch.

Yes.