I don't think the current sense is suicide exactly, but rather (hyperbolically) so sold on a (misguided) belief that you would commit suicide if, per that belief, they were "supposed to" do so. I agree that it would feel awkward to use it about someone who had actually killed themselves, but I think that's mostly because there's an element of (dark) humor to it.
When we say “drinking the Kool Aid” we mean adopting a dumb way of thinking. Not killing yourself, or even harming yourself. Just being stupid.
We wouldn’t say “they drank the kool aid” if someone committed suicide.
More important for present discussion, “The Kool Aid Acid Test” referred to actual Kool Aid, not a generic equivalent.
The Kool Aid marketing team embraced and promoted its countercultural image. Many brands did.
But this left the brand vulnerable when the counterculture became associated with extremism.
Recent parallels to this exist.