Photo booth videos are saving as corrupted/blank files

Having the same issue …

Same as what? Your post makes no references.

… with Photo Booth saving corrupted videos.

It works fine on my Mac?!?

How do you determine that videos are corrupted?

Have you tried recording a movie in QuickTime Player? Should be roughly the same, except the filters.

I don't understand why AAPL has not yet fixed this issue?

Maybe the issue is not with Apple’s software? Then there is nothing to fix.

For macOS troubleshooting, try these:

• How to use safe mode on your Mac - Apple Support. ‘Safe mode’ can help you to determine whether an issue is caused by software that loads as your Mac starts up.
• How to test an issue in another user account on your Mac - Apple Support. If an issue stops happening when you log out of your macOS user account and log in with another, the issue could be related to the files or settings in your user account.

Let us know the results of these tests.

Is there a reliable and free way of recovering the corrupted videos I've already recorded?

If the video is indeed corrupted, then that may be the only data available, and then there is nothing to recover.

If you have a backup of them before the corruption, then you can revert to a previous version.