Speaking of Japan, it, from 1930 until about 1970, was a great example of protectionism. No foreign companies were allowed to operate in Japan until 1960, and even then it was only in uninmportant low-margin industries. Imports were completely controlled by the Japanese government, which imported _everything_ based on what they thought was needed: automobiles are something that were almost never imported, for example. China today is less protectionist than Japan at it's peak but still many factors more protectionist than the US. For example, one cannot directly open a foreign business in China. They must work with a domestic company that takes half their profits.
All this isn't to say that the US isn't protectionist, or that protectionism is even bad. But your claim that "The U.S. has a long, proud history of protectionism" really has no qualifying element, and in fact all the qualifiers seem to go in the opposite direct that they should.
That said, yes, the 1A implications are thorny.
Would the FCC allow a VoRussia or VoChina radio transmitter in the US whose sole purpose was to push Chinese or Russian propaganda?
Probably in a war declaration we could shut them down, but what about peacetime?
I'm sure they already do? https://en.wikipedia.org/wiki/RT_America was operating right up until the imposition of sanctions.
But that said, looks like all the Biden admin needs to do is set up some sanctions (for whatever reason) and put TT under that umbrella and voila!
Hell, look at something like The Economist. They're regarded as an excellent news source, which makes their efforts at pushing a certain economic and political POV far more successful than if they pushed it so hard that they weren't a good news source.