After some fiddling I found that the moodle/theme/boost directory I had after the update using Softaculous had more files and was a little different from the one in a clean 3.8.2+ install, so I replaced it with the one from the clean installation and after a few "undefined" messages and Ctrl-F5 the site started working. Make sure you actually remove the old moodle/theme/boost directory because if you just rename it the site breaks.
Installing and upgrading help
Grader stuck on "loading..." in Boost and Classic themes
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