Same for me, on Vivaldi. Cookies are allowed, though. It is some privacy setting I cannot find or disable, not sure what exactly.
It is sad that the Twine or Sugarcube authors ignore this problem, though it exists for years and people regularly report it on the Twine discord. I can access local storage fine, and other websites/games can do to, e.g. Paperclip AI. It should be possible for Twine to get it right, too.
John Ayliff, your game Seedship does work fine though. Is the difference that you do not use any save features there?
Sorry for the rant, it’s just so unnecessary and disappointing.