On my Apple TV, I opened the TestFlight app, selected Plex Experience Preview, selected … More, then selected Stop Testing. Then, double-click the “TV” button on the remote and swipe up the TestFlight app.
Then, I opened this TestFlight link on my iPhone, and Accepted the invitation (it was previously showing as “full”).
Re-open TestFlight on the Apple TV, and it’s there!! Hooray!