Hi know this is an old post, but I thought I'd chime in. I've manage to do this, and it pretty easy really.
I'm using Vimeo, and I have used the below iframe inside Squarespace's video block, not a code block. But instead of adding the link, you can click <> and insert this code.
I am using it on our new SquareKicker website for our learn page here: https://squarekicker.com/learn
Just swap out the vimeo number for yours. See screenshot below for example.
<iframe src="https://player.vimeo.com/video/466007910?autoplay=1&loop=1&autopause=0&background=1&color=ffffff&controls=0&portrait=0" width="800" height= "500" frameborder="0" allow="autoplay; fullscreen" allowfullscreen></iframe>
It also will auto play on mobile. You can adjust the settings for controls back to 1 instead 0. And muted is background=1, so if you want sound change that, switch it to 0.