In the current free version it would require some HTML. Using the same method applied to a page hero:
https://docs.generatepress.com/article/page-hero-background-video/
In this case you would add a HTML block inside your Container Block with this markup:
<video loop muted autoplay poster="URL/TO/poster.jpg" class="background-video">
<source src="URL/TO/video.mp4" type="video/mp4">
<source src="URL/TO/video.webm" type="video/webm">
<source src="URL/TO/video.ogv" type="video/ogv">
</video>
Then give the Container Block an Advanced > Additional CSS class of: video-container
Then add some CSS to your site like this:
.background-video {
position: absolute;
top: 0;
right: 0;
bottom: 0;
left: 0;
opacity: 0.5;
}
.video-container {
position: relative;
overflow: hidden;
}
.background-video-content {
position: relative;
z-index: 1;
}
video[poster] {
object-fit: cover;
width: 100%;
height: 100%;
}
It may require a little tweaking.