There is not a process to "request" camera access–instead, applications simply try to access the camera. ImageJ need not know about the approval process to try to access the webcam.
You cannot add an app that has never tried to use your camera to this list.
Cameras either have or don't have these features.
Pan (side to side adjustment),
Tilt (crop & enlarge),
or Zoom (up & down adjustment)
This is shown as P/T/Z or PTZ on feature lists.
Apple's built in FaceTime camera has none of these sadly, you will have to look at the specs for any external camera you have to see if it does.
While there is some ...
An alternative solution to crgarridos and Nics that worked for me is to reset NVRAM/PRAM.
My System Integrity Protection (SIP) is (and was) disabled and should stay that way (running on Catalina-Patch).
I found the solution in this article.
Open the Image Capture app and select the camera. You can manually import images or change the settings. This app manages the cameras and bulk image import from storage media for macOS Catalina and lower.