Is there sort of Audit log for a child site? Especially for updates to plugins and themes?
If a site goes down with error 500, it is usually caused by an update. Official WP guide is to disable all plugins and search for the culprit.
If I had a list of recent updates, It would be far more easy to pinpoint the culprit.
You can have a look at the Activity Log Extension that using the plugin:
Personally I have automatic updates disabled everywhere, so I should know what I’ve updatet very recently. If I don’t (or it has been a few days with multiple updates), I just open (S)FTP and check the timestamps of the folders in /wp-content/plugins/ and wp-content/themes/ to determine recent changes. Besides that I examine the PHP error log, because most errors show the component that’s causing it.