I'm looking to use the Paragraphs Drupal 8 module with a decoupled installation of Drupal 8 but would like the structure made in the admin area to be output in the JSON API responses.
How can I modify the JSON API responses from Drupal 8 to include this page structure data?
If anyone wants to know, having it decoupled & outputting structure information is a requirement I've been given.
It sounds like you want a compound document, the JSON:API mechanism that provides other referenced entities in a resource (e.g. a "page" content node that references other paragraphs). This is done via adding an include query parameter with a value that refers to a field's relational ID. An inclusion request will add an included array property with the related entity resource objects.
See the docs on Includes in the JSON:API docs for more concrete examples in action.
Since you mentioned it, ordering included resources isn't possible (IIRC); you might be able to infer order based on the Paragraph field. JSON:API is designed for minimal configuration and maximum adherence to the JSONAPI spec so you're limited to a couple of mechanisms to modify the output of the structured data.
included is the actual order corresponding to the paragraph-field deltas, but now I am wondering if I can rely on it? This is not specific to paragraphs, but to all multi-value fields, I guess.