The Fatal Error was:
Fatal error : Uncaught Error: Call to undefined function wp_is_json_request() in /var/www/vhosts/mywebsite.com/wordpress/so-content/plug-ins/cookie-notice/includes/frontend.php
Fake website url, but actual error from one of my websites.
Plug-in update for : Cookie Notice & Compliance for GDPR / CCPA Version 2.4.5 | By Hu-manity.co
This is a plugin conflict, it is possible that the plugin you installed has included some features in the update that somehow conflicts with your other plugins.
You can change the plugin you use to manage cookies (not recommended because it’s a ton of work testing an alternative if that one works for you) or reach out to the developer mentioning you use ClassicPress in your support request so that they can fix the problem (that is the solution I recommend because not only it solves your problem but makes the dev aware that the plugin works with CP and has a userbase of CP sites).
It looks like the plugin falsely claims compatibility with WordPress 4.7. The undefined function in this case is wp_is_json_request, which was added in WordPress 5.0. ClassicPress doesn’t have it, and that’s why it’s causing an error. I submitted a support request to the developers to verify the compatibility of their plugin.
In the long run, these missing functions will be included in ClassicPress v2.0 as we re-fork the core based on WordPress 6.1.
The easiest and fastest option right now is to roll back to the previous version that worked. You can download the previous version at the bottom of this page:
https://wordpress.org/plugins/cookie-notice/advanced/
Thanks Elisabetta & Viktor. 