You've misunderstood. I had cleared enough space for the update to give the go ahead. Then during the installation it ran out of space and got stuck in an infinite restart loop.
So clearly the Catalina update requires much more free space than it says it does before allowing the installation to continue. Just poor software development and lack of testing.
Here's a Reddit thread of people with the same problem: https://www.reddit.com/r/MacOS/comments/deuwsa/help_stuck_in...