The shared banner video remains unchanged because Elements does not expose safe preload/poster/autoplay controls for it. The biggest future improvement would be replacing it with either:
A lightweight static poster image, or
A shorter, compressed, muted video loop.
After publishing, test with a cold-cache mobile connection to compare initial video requests, transferred bytes, LCP, and repeat-navigation caching.
Dan is right that Video already has a poster/thumbnail and autoplay options (plus mute, loop, and controls for mp4). Worth checking those on the banner video first if you have not already.
I looked at what the component actually exposes. The one clear gap for the cold-cache / LCP case is a preload control (none / metadata / auto). That is not in the Video settings today, so I have flagged it for Ben.
If you are after a true background video treatment, Container is the separate path for that, rather than stretching Video into a banner.
Happy to dig further once you say which bits still feel missing after trying poster + autoplay.