I just tested this on my Grav site; it worked without an issue. (Ubuntu 16.94, Nginx 1.13.7, PHP-FPM 7.0.22) Given that, I’d say the documentation is still spot on and I would be more prone to questioning something in the server’s or site’s configuration. I’m guessing this is a shared host if you don’t have SSH access. Are you using a control panel (cPanel, Plesk, etc.) or just FTP/FTPS (since you don’t have SSH, that should mean you aren’t using SFTP, though FTPS could still be a thing).
I want to make sure I am understanding you and to clarify we are on the same page: when you say phpinfo is being displayed after adding code to the file, you are adding it to a file called “setup.php” which exists inside of /homepages/40/d564426001/htdocs/, correct?
If so, then we at the very least know that the file is being read and Grav is either not processing the variable change, or something is not letting the change be made on the host.
I want to narrow this down to one or the other.
When you say the latest Grav update spawned the error, did you update the site to Grav v1.3.10? What version did the site update from? Were there any other changes with the update? Given that it was working fine before the update, this would strongly imply to me something site-side rather than server-side, as the server was letting the log files be written to until the update. The change to 777 shows it is not ownership/permissions related, and the Apache/FCGI setup is pretty standard. I’m surprised the site would beginning as www-root rather than a user if it is a shared host, but beyond that, it sounds normal.
Are you using any Grav plugins, have you made any changes to other Grav source files or to the site’s config, or is this a relatively clean install? (I killed my site for a time by disabling a single option and only managed to get things running once I turned it back on again; it’s why I ask.)
Would you be able to test a fresh Grav install of the installed version to see if it persists there in a subdir?
A common troubleshooting technique with WordPress is to disable any and/or all plugins. Is there perhaps a caching plugin at work?
Are you using Memcache or any of the other caching options?
Can the site create posts/pages?