I’m pretty sure you don’t have to file a flight plan with the FAA, given wind currents it would be nearly impossible to know how fast or direction the balloon would be traveling.
It’s also not atypical for a hobbyist balloon to circumnavigate the globe and do so multiple times.
Typically, the hobbyist balloons are transmitting a radio signal that is monitored by a local ham radio club or operator mainly for educational and recreational purposes.
Back over a year ago when the Chinese Balloon was flying over the USA, we had a lengthy discussion on FR about this very topic and it was determined then that no FAA flight plan is required and quite frequently these hobbyist balloon due circle the globe multiple times.
Here’s a couple of articles you might find interesting from last year during the Chinese balloon fiasco.
“Back over a year ago when the Chinese Balloon was flying over the USA, we had a lengthy discussion on FR about this very topic and it was determined then that no FAA flight plan is required and quite frequently these hobbyist balloon due circle the globe multiple times.”
Yes I remember that discussion. It was a learning exercise for me.