I logged in to do some updates and received an error message about PHP. There has been a critical error on your website. Please check your site admin email inbox for instructions.
When you get that polite 'white screen of death', you'll find the problem in the error.log file in the root of your site (perhaps in the error.log file in wp-admin, if the error was caused by an admin-level program).
You can renamed the plugins folder to temporarily disable all plugins. But the error.log file will tell you exactly where the error was caused. If in a plugin, rename that plugin's folder (in the plugins folder) to temporarily disable it. Then you can proceed from there.
You might get a message in the email of the site owner (as defined on the Admin, Settings screen), but it's faster just to look at the error.log file.