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.
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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?
EDIT
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.