Andrea,
Your video is very illustrative.  I know nothing about GOP except that when working on bluray media, it was necessary to include gop in the opts files.

I attach a video: the first part is made with an mpeg proxy (I have
not seen its GOP), then there are examples without proxy with X11 and
with X11.opengl. The file consists of screen capture with vokoscreen
and gave rise to mp4 files with GOP but at 250. With proxy I am fixed
at 30 fps, in the other cases we speak of very low fps.

I made a background rendering video but what I am trying to show is explained below url:

What I am attempting to demonstrate in the video is when you playback and get to a transition slow point, the framerate achieved is only 20 instead of the expected 30.  However, if you use background rendering, then it will stay at 30 framerate because it only has to re-rendering during playback the frames that have been changed.

When you do background rendering, what it does is render each frame individually so you will end up with potentially hundreds of single files in /tmp called brender0001, brender0002, ....  Since these are usually JPEG files, you can view them too and swap one out (I think but never tried this.)

Page 21 of the old cinelerra manual discusses this too.