Hey Eliot,
Yeah, you can do that easy enough — just use the <video> tag in HTML, chuck in your autoplay, muted, and loop attributes, and you’re good to go. That’ll make it play automatically and loop forever without sound.
Just make sure the video’s either covering the whole page via CSS or inside a div set to position: absolute or fixed, depending on how you want it layered. Also, don’t forget playsinline for mobile if you want it to behave.
If you need it to sit behind content, you’ll just set the z-index stuff right and maybe throw object-fit: cover on it so it doesn’t go all weird with scaling.
Let me know if you want a snippet