It's 100% about controlling the narrative. "Young Americans are turning against Israel — and you can thank TikTok" https://forward.com/opinion/574346/freepalestine-tiktok-isra... Can't have that happening in the US. The right to brainwash kids is a right reserved to the American billionaire class, their purchased politicians and lobbyists. You can talk about "geopolitical risks", "security issues", and "reciprocity" all you want but it doesn't hide this fact.
(1) trade protectionism that is about protecting the right to profit off of manipulation of American youth to favored actors, rather than disfavored foreign actors (whether disfavored because their country doesn’t allow American firms the same power in their countries, or for other reasons) or
(2) totally not trade related, but speech related, and about reserving the right to manipulate American youth to the exact same favored actors discussed in #1.
If TikTok is banned for geopolitical reasons, reciprocity reasons or whatever you want to call it, that doesn't change anything about free speech in America. It's not the unrestricted speech that was deemed a problem with TikTok, but rather the specific geopolitical risk (or whatever).