Hello Fr3dC0rt35,
Thanks for reaching out on the Apple Support Communities. Having your webcam working for both video and audio is important to be able to stay connected.
As this issue began following the update to macOS Catalina, you'll need to verify that your webcam is compatible with the macOS Catalina operating system. This link will take you to their support page: Submit a request – Logitech Support + Download.
If you find that it is supported, you'll want to continue with these troubleshooting steps:
1 - Quit all apps. If an app will not quit, follow these steps to force it to quit: How to force an app to quit on your Mac.
2 - Restart your Mac: Go to the Apple menu in the top left corner of your screen > Restart. See if there is any change.
3 - Restart in safe mode and test again: How to use safe mode on your Mac.
4 - If still occurring in safe mode you’ll need to create a new user, sign into that new user with your information, and test it out again. This article will show you how: How to test an issue in another user account on your Mac.
All the best.