furo requires webpack since version 2021.11.12 and was recently updated in 7b890d5933. Without this dependency, the built package is broken as it is missing some important files. This can be seen when trying to build kitty on Linux. webpack doesn't work correctly in nixpkgs, see https://github.com/NixOS/nixpkgs/issues/42275. I wasn't able to fix this.
To make furo build correctly again despite the broken webpack, I switched to fetching the wheel instead of the source from PyPI, which has the necessary files already generated.
I also added a small test to make sure that this directory won't be empty again in the future.