On linux you may be able to set it up with fmpeg and v4l2loopback (create a v4l2loopback device and have ffmpeg grab your input, crop it, and output to that dev

On linux you may be able to set it up with fmpeg and v4l2loopback (create a v4l2loopback device and have ffmpeg grab your input, crop it, and output to that device). Maybe less overkill, but probably more involved to set up though so OBS is probably your best choice unless it is really too heavy.