I can find the previous localStorage api data in ~/.config/google-chrome/Default/Local Storage directory. I see that these are sqlite files which I can browse w
~/.config/google-chrome/Default/Local Storage
For Firefox which now use the same format as Chrome for addon they are saved here:
C:\Users\Marc\AppData\Roaming\Mozilla\Firefox\Profiles\x5jztslz.default\browser-extension-data\