Website unstable after updating multiple plugins

When I first began working on my company’s WordPress site in May, there were several plugins that needed updating. From the WordPress Updates page I selected multiple plugins and clicked Update Plugins. Afterwords the WP Admin page went down. I couldn’t access the dashboard or the login pages on Chrome or other browsers. A couple of the pages on the site were also down, all returning a 500 Internal Server error. I told me supervisor who says he didn’t see anything in the error logs, but refreshed the server (?) which fixed it. Since then, every once in a while the wp-admin page will go down again with the same message. Sometimes it is after another plugin update (recently the culprit was Yoast SEO) but sometimes it seems to happen randomly overnight. I realize it when I get in, in the morning.
My supervisor says this issue only came up after my updating multiple plugins at once, but we don’t know the cause due to it also happening without updating plugins.