We keep reaching for straws here when bringing up themes (although there have been isssues with themes in the past, but don't think any of those issues affected backups). Doesn't have any reference in the error ... concentrate on the error.
Clue: moodle site in a directory of main site - means you are running something else ... like a WordPress?
And ... never able to get autobackups running ... at all ...
So let's quite trying to hide the provider - if they are doing such a terrible job supporting Moodles then community users deserve to know, And, you might have to seek another provider that is more Moodle friendly. Since your site is already on the internet and accessible (am assuming it's not a private anything) then why hide provider? You're not training for a government entity on espionage or weapons or such, are you?
So who is the provider?
Sometimes, providers have FAQ's/Docs/their own forums available to the public ... sometimes they have private forums for customers only. Would do some 'leg work' for ya IF I knew the provider.
'spirit of sharing', Ken