Qualifications for this response: none in that I don't host on SiteGround ... but I have been running Moodles a very long time.
I'd say that "Site tools at siteground" doesn't follow what installation docs of moodle say to do with moodledata directory - which is to locate it outside of webservers document root - where web pages live but accessible to the web server user such that it is readable and writable.
Example: moodle code is in /var/www/html/
moodledata is in /var/www/ because the web server user home directory is /var/www/ and can see, read, write, whatever to moodledata and any folder/file contained there in.
Since you are using a tool provided by Site Ground, shouldn't Site Ground technical support actually support?
Ask 'em ... feel free to come back here and share what they did/said for others who are hosted on Site Ground and attempt a Site Ground tool for Moodle.
Maybe these will help: