Expose default gutenberg block styles in WordPress rest API

Question

We're using the WordPress REST API to power a static site. The site is "headless" in the sense that we don't use a WordPress theme; we rely on the content being exposed via the REST API.

Some of the default Gutenberg blocks - the Buttons block for instance - have styles with hashed class names associated with them that don't seem to be exposed in the API. This would be kind of ok if the class names were predictable but, since they aren't, we have no way of providing the styles on our end.

If we do render the blocks in a theme, the styles are rendered in the footer

Here's an example of the style block for the default Buttons block looks like in a WordPress theme

The Rest API endpoint exposes the markup in content.rendered (including the classnames) but no styles

Is this expected behavior for using Gutenberg and the WordPress REST API? If so, is the correct solution to expose the styles via a custom field (for lack of a better term) on the API?