I heard in war time Korean armed forces report directly to a US general, including during the recent martial law.
In the event of a conflict on the Korean Peninsula, American and South Korean forces are supposed to operate under a single multinational command known as the Combined Forces Command.
IIRC, this command has always been led by the sitting USFK CG with a South Korean four star as his DCG.
However, very doubtful USFK is involved in South Korea's current domestic political woes in any meaningful way.
They know the South Koreans will keep them around after the current political crisis is resolved regardless of who or which party prevails.
So there's no need or incentive for USFK to get involved or even pick a side.
It's practically impossible to find US media talking about US internal issues.
I'm curious what US media outlets you're referencing?
Even here in the People's Republic of California, issues like homelessness and income inequality are frequently covered by the media.
Granted, meaningfully addressing these problem sets is a whole other can of worms.