This is possibly the missing piece: https://jira.atlassian.com/browse/CONFCLOUD-65654
For those wondering if full-width is possible through the API, it seems that it is possible through the properties endpoints (here) and when you create new content (here) though the documentation for the create content endpoint does not say so. I found this post which suggests that it is possible through the create content endpoint (here). I made this work in my side project and will put an example of the body I sent below (python code) in case anyone makes it here and is looking. The “content-appearance-draft” and “content-appearance-published” are the properties that need to be set for the page width to appear full.
body = { 'space': { 'key': confluence_space_key }, 'ancestors': [ { 'id': confluence_ancestor_page_id } ], 'type': 'page', 'title': confluence_page_name, 'metadata': { 'properties': { 'content-appearance-draft': { 'value': 'full-width' }, 'content-appearance-published': { 'value': 'full-width' } } } }```