OK, luckily I’ve made a healthy back up before I uploaded everything.
I opened the SQL-file and find/replaced all the localhost-parts to https://www.domain.com.
Now everything seems to work. Don’t have a back-up? Bad news, unless you can still modify it in the online phpmyadmin.
I suppose I shouldn’t have put the localhost-address in the settings page (as website and blog-url) while the site was still local back then, although that makes sense in a way.