I can see two things in your latest screenshot 1) the backup file appears to be 715.7 MB and 2) the XHR request is getting a 504 Gateway Timeout after 5 minutes. So maybe the the problem is that because the course backup is large a timeout is being exceeded.
Check PHP's max_execution_time, shown in PHP info. This may be 300 (i.e. 5 minutes). You could try doubling it.
In PHP info also check Server API, is it "FPM/FastCGI"? If so, then the next thing to check is Apache's TimeOut setting and try doubling that. This will be set in a .conf file somewhere, you may need to use grep if there are many files to search.
When changing any settings you probably need to reload or restart the corresponding service (e.g. systemctl restart httpd or systemctl restart php-fpm).
If your server is managed for you then you may need to contact the hosting provider for assistance with this.
If I'm correct about the size of the course backup you may want to try using Moosh to perform the restore at the command line as this avoids some issues with timeouts.