How can I fix Photo booth?

1 - Apple Support is not here as the only person on these Forums are users like you and me

How to use Apple Support Communities

2 - If the user what Apple Support >> Get Support Choose a product and we’ll find you the best solution.Start now and open an Apple Support Ticket as they are Apple Employees to deal will these types of issues 

3 - Suggestion predicated on Profile attached to this question >> " MacBook Pro 16″, macOS 13.1 "

4 - Update this computer to the current version of Ventura 13.3.1

Both links below pertain to keeping the computer up to date as they bring some Big Fixes and Security Updates

Once that is done, if not already - Then Test again as the issue may have been fixed

Keep your Mac up to date - Apple Support (CA)

About the security content of macOS Ventura 13.3.1 - Apple Support

Photo Booth has never seemed very reliable.

I can only recommend that you use Quicktime Player to record your videos instead.

File->New Movie Recording, make sure that the proper microphone is selected, and there you go.