When I disabled the full site integration everything worked again.
I managed to still use the CDN through a plugin instead, so each resource url’s points directly to the CDN instead of being transparent in the html.
I didn’t tried disabling Jetpack’s CDN, but i think the issue is not directly related, because even the connection check was broken.
Maybe something related to stackpath “proxying” the site?
Fortunately, as I said, everything works again.
We can use this data to find out what’s happening, if you want to.