@maxime-guitet Hi , I was facing a similar issue when I was trying to load the self-service account page in Iframe in our application.
Our setup was same as yours. Fusion auth hosted on auth.domain.com and the iframe is hosted on app.domain.com. So they both share the same top level domain. The issue regarding the X-Frame-Options: Deny being not available in every request was solved by adding referrer policy attribute to the iframe tag.
The final iframe code looks like below
<iframe
src="https://auth.domain.com/account/?client_id=<your id for application>"
referrerpolicy="strict-origin-when-cross-origin"></iframe>
Hope this helps!
Regards
Vatsal