How can I get post content from WordPress API and maintain or recreate positioning?

I’ve created a Next.js app and it’s my intention to pull post data from my WordPress.com site via the public WordPress API. I’ve gotten the HTML content of my posts just fine at this endpoint:

https://public-api.wordpress.com/wp/v2/sites//posts

but aside from minimal inline styling there’s no way to recreate the structure of the original post – ie, columns, galleries, grids, blocks, etc.

I can of course apply my own CSS to adjust fonts, colors, responsiveness, etc, but don’t I need the positioning styling to make sure that the post is as the original author intended it to be? Columns in the original post, for example, are not respected because the class names that denote them in the API response don’t exist anywhere in my CSS. I could conceivably use these class names to recreate similar element positioning, but this seems like an awkward and messy approach.

I’ve tried manually adding the stylesheets from the post’s page, but still the styling from the page did not appear to match the class names from the API post content.

I expected that the API response would include some way to at least recreate the original structure of the content from the post so that my app can position the content similar to how the author did. Or is this just not possible? Thanks in advance for any help!