Making Logi Capture work in macOS Catalina and macOS Mojave
https://www.reddit.com/r/MacOS/comments/ijzp9f/logitech_web_cam_owners_logi_capture_software_not/
Download 2.0.200 from the link below:
https://support.logi.com/hc/en-us/articles/360025141614
Direct download link: https://download01.logi.com/web/ftp/pub/techsupport/capture/Capture_2.0.200.zip
This version asks for permissions and works as expected.