Completely stopping people from using open source models is impossible, but if it became a federal law there could be incredible pressure exerted on US companies. For example, OpenRouter might be compelled to not accept open source requests on threat of fines.

I'm just a guy who writes code and geopolitics and big business is usually above my head

That said, I have a suspicion that if the US exerts that kind of pressure on US companies, they will just pivot to using offshore contractors that are doing the things they want