This camera?
https://www.logitech.com/en-us/products/webcams/c270-hd-webcam.960-000694.html
Did you manually download the camera's drivers directly via Logitech's website? No third party tools or installers.
Did you also download and install any related Logitech Software options? If so which ones? Double check any configuration settings available therein.
How are you connecting the camera to the computer? USB port or via some USB to TRS adapter? What make and model adapter if any?
Setting "noise suppression" aside for the time being - can you get the c270's microphone to work by any means?
Are you able to test some other known working webcam/microphone on your computer?
Or test the c270 camera/microphone on another known working computer?
Determine if the lack of audio/microphone follows the camera or stays with your computer.