This post mentions simply restoring the WSL directory partially restored WSL, but with some functionality issues. This post gives generic information for how to back up and recover a linux installation. This post says that %appdata% is in fact moved into your Windows.old folder, which is created after reset and contains your "old" files.
What information might have gotten lost in the first posters experiment? Are there some registry settings or configuration files that would allow simply restoring the Linux root directory (
%USERPROFILE%/AppData/Local/lxss) to work?
My question was marked as a duplicate of How to backup (WSL) Linux Subsystem for Windows 10, before system reset or reinstall?.
However that question was only about how to back up the installation--basically tar it and save it somewhere. I explicitly ask about how to restore it.