No comment on the central message, but I actually like "unalive" as a word: it feels vaguely Old English. "Commit suicide" always felt a little stilted as a two word phrase.
"Commit suicide" in TikTok NewSpeak isn't a single word. It's still two: "unalived themselves". "Unalive" means "kill".
Plethora of options, really
The author uses "dying by suicide", which is better semantically, but still a bit wordy. Another option might be to verbify "suicide".
The Old English verb form would more likely be "dealive", with "unalive" being an adjective.