Getting the texture of a window when using a compositor is an nvidia specific limitation. When gpu-screen-recorder supports other gpus then this can be ignored.
Nvidia 515.57 supports nvfbc direct capture with mouse capture. Check if driver is equal or newer than this and use mouse capture in such situations (with direct capture) supports nvfbc direct capture with mouse capture.
Allow recording all monitors/selected monitor without nvfbc by recording the compositor proxy window and only recording the part that matches the monitor(s).
Allow recording a region by recording the compositor proxy window / nvfbc window and copying part of it.
Resizing the target window to be smaller than the initial size is buggy. The window texture ends up duplicated in the video.