This is just a note to my future self - no assurances it will work for you!
This fix isn't permanent and will be overwritten by the system arbitrarily, hence why I wrote down the steps and script that worked for me here so I can easily set it again. The previous sentence was true until macOS Sonoma (14) was released, which now allows TouchID for sudo to persist across updates and restarts. The script will automatically detect if you are on Sonoma or later and apply that permanent change instead of the earlier, non-permanent fix.
Copy + run the line below.
curl -fsSL https://gist.githubusercontent.com/uncenter/604233698c41f1c54079760b93fbabf0/raw/x.sh | sh