My previous version has flaws. It works well for opaque GIFs, but OpenCV is famous for not being good with transparent images. So instead of OpenCV I use imageio for GIF iteration and PIL for adding GIF frames to the static background.

Why do more?

The original algorithm left these artifacts, look at the cyan block on the intersection of GIF frame and a darker abstract part:

Solution

The code is pretty much the same as here How to add GIF to a static background (Python + OpenCV). Video Generation series (Part 1), except for the loop itself:

    frame_index = 1
    while True:
        if frame_index < gif_length:

            # get a frame with imageio
            foreground = gif_reader.get_data(frame_index)
            
            # convert it to PIL.Image
            fore = Image.fromarray(foreground)
            
            # making a new image - background + GIF frame
            frame_path = f'temp/{frame_index}.png'
            back = Image.open(background_image, 'r')
            back.paste(fore, (0, 0), fore)
            back.save(frame_path)
            
            # for OpenCV to add it to video
            frame_to_write = cv2.imread(frame_path)

            video.write(frame_to_write)
            last_frame = frame_to_write
            
            total_frames -= 1
            frame_index = frame_index + 1
        else:
            break
    while total_frames:
        video.write(last_frame)
        total_frames -= 1

Comparison

In particular detail that indicates the issue is now gone:

Happy as I can be.