One of two things, either that is not the path for php-fpm.sock, and you should edit the path in nginx config. Otherwise it is permissions. Verify that the file at that path exists (only exist while service running). Then check permission. Php config can help set default permissions of a sock file, since it respawns with default every time you reboot or restart the service.
The Ubuntu instructions are highly streamlined because of effective default configs that I assume don’t exist in Debian or are just different.
Systemctl status php-fpm will tell you the path of current php .sock file and its name (sometimes www.sock). Verify that path, and configure nginx accordingly and verify nginx has permission to the sock file.
See my CentOS guide which already has examples of these steps, you will have to adapt them to your environment.