Hi there! Apologies for this long process, the app that supports our Photo Booth is still working on developing a fix for this problem. But for now, here is a step-by-step way to save videos directly to your phone!

Tap the Download Capture icon on the capture page

Wait for the capture to load in a new Safari window
Once the capture has loaded and is playing, look for the minimize window icon (it looks like two overlapping squares) in the top left corner of the screen and tap it
Once the video is minimized, it will still be playing in the corner of the screen. Tap the share icon at the bottom of the Safari window
From the share menu, select Save to Files
Choose where you want to save the file in the Files app (e.g., "On My iPhone" or iCloud Drive).
Tap Save in the top right corner of the screen.
Once you have saved to files, simply open the files app and save to camera roll!