If the recording screen stays on "processing your video" for longer than a few moments, you can safely refresh the page. Your existing recordings are saved automatically, so refreshing won't cause you to lose any answers you've already recorded.
After refreshing, open the video interview again through the same link and continue from where you left off.
Note: If the issue keeps happening, check your network quality — a slow or unstable connection is the most common cause of a stuck upload.