Akeeba Backup IS NOT responsible for this issue. This problem came from another update, possibly "Regular Labs - Sliders". In short, another plugin you updated requires Joomla! 3.9 but you only have Joomla! 3.8 on your site. Moreover, that plugin, unlike Akeeba Backup, had no checks whatsoever to prevent installation on an unsupported Joomla! version.
Now, if you'd like, I want to explain in detail what happened.
Joomla! 1.0 up to and including Joomla! 3.8.13 had a class called JFile. This class was renamed to Joomla\CMS\Filesystem\File in Joomla! 3.9.0, a version of Joomla! newer than the one you are using on your site. This is part of a series of changes made in Joomla since version 3.4 and will continue until Joomla! 3.10 to pave the road to Joomla! 4.0 and ensure a smooth transition. I know all about that since I was one of the eight people who drafted the roadmap to Joomla 4 back in June 2015 in Prague.
I not only know about these changes,
I have personally created a handy table which documents these changes. It'd be silly for me to use a class in my software which is not compatible with the Joomla! versions my software supports -- Akeeba Backup 6.3.3 supports Joomla! 3.4 to 3.9 inclusive, i.e. it is compatible with the lowest common denominator, Joomla! 3.4. After all, I have already done the hard work to avoid breaking sites because I accidentally used a class not available in a supported Joomla version, right? :)
On top of that, I know that your site would break if I start using a renamed class in a version of Joomla which does not have it. This is why all of my software performs a Joomla version check before it's installed on your site. If you are running a Joomla version not supported by the software you're trying to install or update we tell Joomla to cause the update to fail WITHOUT replacing any files on your site. I'd say it's best to tell you you can't upgrade our software until you upgrade your site than leaving you hanging out to dry with a broken site.
You
never, ever, ABSOLUTELY EVER need to be afraid updating Akeeba Backup and Admin Tools. I am personally vouching for the testing I have done and automated measures I have taken to ensure that your site WILL NOT break when you install
my software. I go one step further. I first install my software on my own site, my only source of income, and only then do I publish it for you folks to install.
In your case it'd look like Peter (Regular Labs) -- or another developer of a plugin you updated but you didn't tell me about -- decided to upgrade his code for Joomla! 3.9 but did
not include a version check on update. As a result you installed software that requires Joomla! 3.9 on a site that still runs Joomla 3.8. Hence your problem.
On that note, you can always use the backup you have taken with Akeeba Backup to restore your site to a working order WITHOUT having access to your site. If you are not sure how to do that please check
this video tutorial.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!