Recover MacBook with full disk after failed OS upgrade
There are a few good suggestions here. In the end the approach that solved my problem was starting recovery mode, and deleting a lot of unneeded files from my hard disk. 
(There was a lot of leftover stuff in Library/Application Support from applications that I have long ago uninstalled.)

After I freed up ~20GB of data, I could launch a reinstall of MacOS from recovery mode, which did the trick.