For adding classes to body try this in the footer of the page settings.
var element = document.querySelector('body');
I hope to see the ability to add classes to the body of any page. Just a textfield and maybe support for multiple classes with a comma would suffice. The idea of styling the body doesn’t address the issue in any way.
The classes would be used for scoping and specificity I’m curious what you think, and if it’s low enough hanging fruit for you to tackle anytime soon. In my opinion this is a missing feature. If it’s cool to add a class to a bric or a bloc it’s equally beneficial to add a class to the body.