All right, I figured out what went wrong – and I think I know why.
Everything after the salt-keys in wp-config.php got deleted, and I guess this happened because I have Norwegian language as default, and a comment in there stating that it’s forced to Norwegian (this is done by the WP-team).
My guess is that the function that parses and upgrades wp-config.php doesn’t understand anything when it gets to this comment, thus crashing and breaking the file.
Fix wp-config.php and your site should be fine