Embedding coda with Google SSO (not Google Sites)

I’m trying to embed a Coda Doc on a website with Google SSO. The idea is to log into Coda either through the same process as the website or through an additional login in the iframe.

I do not want the Doc to be shared Publicly, i.e., anyone with the link can access it.

Alternatively, I can build an API integration, but that does not work as there are limitations regarding fetching pictures, rich text, etc.

Can it be done somehow?