It wasn’t an obvious journey figuring out that I had to download the live build stuff in order to enable compilation.
There’s no indication within the Projucer itself that you have to do this first, at least not until you dig around and hope to find something to trigger the download of the files.
I managed to find this https://juce.com/discover/stories/projucer-manual#8.-live-build-engine , but still it could have been just a hint more obvious from the UI.