How can I retrieve the original content in a page via REST API, content that I pushed myself also via API?

To get the raw content, you need to pass the context argument as edit. This is the version of the content that’s used in the editor, and should match the raw data you originally sent. This version of the content will be accessible at content.raw.

Note that using this context may require the request to be authenticated, as the current user will need permission to edit the post to see the raw content.