The block's HTML is passed along to the render function of a dynamic block. When using ServerSideRender the block's HTML is not made available to the render function, only it's attributes are passed along via the API request:

https://github.com/WordPress/gutenberg/blob/master/lib/class-wp-rest-block-renderer-controller.php#L149

One can access the block's HTML via the block's attributes (that would enable me to pass the html to the render function by adding it to the attributes), but that html content does not include nested blocks as they are within HTML comments:

content: {
	type: 'string',
	source: 'html',
},

I've tried accessing the block's "raw" unparsed HTML in my edit function but have not found a way to do so, is this exposed in any way?