You've found your problem ...
"Fatal error: Maximum execution time of 30 seconds exceeded"
One must increase max_execution_time in the configuration of php (php.ini)
I see by information shared in a previous post it appears you are remotely hosting and don't have access to the php.ini OR you've not read up on how to use a php.ini on your remotely hosted system. Providers normally provide how-2's docs on such things. Check with provider docs/helpdesk etc. for how to change max_execution_time variable.
You could try: php_value max_execution_time = 120 in .htaccess but if that results in an error 500 your package is restricted so then one will have to use a php.ini file in the moodle code directory (or maybe serveral moodle code subdiretories) to be able to get php scripts a longer time to run.
In php.ini file:
max_execution_time = 120
Changes to php require restart of apache.
BTW, the server PHP info in Moodle does show what php.ini file it's using. If that is NOT in your space, again, check with provider.
Not sure a restore would fail IF it could not find a file ... it might pause a long time, however.
Next time ... report where you host your Moodle. That will at least give someone attempting to assist information and they might be able to locate the providers FAQ/how-2 doc on the issues (that's really going the extra mile as a customer could do the same with very little effort + you get to test how reponsive your provider is).
'spirit of sharing', Ken