Quicktime and Logitech

This seems to be a pretty good tutorial: https://greatrecording.com/record-video-quicktime-player-for-mac/

It seems that the camera must be compatible with Quicktime Player, and that compatibility list may not be the same as iMovie or Final Cut.

If you are just having trouble choosing the camera to use, here is the relevant excerpt from the article:

The Camera, Microphone and Quality selection menu is opened by selecting the inverted caret next to the record button. The computer’s available cameras (video sources) and microphones (audio inputs) are displayed, as well as the option to select either High or Maximum quality.