I've tested this by printing the local storage itself from the game, and I can see the entry of other games made by me.
I'm not sure if the local storage is also shared between games of different authors.
If u have done a game that uses local storage let me know so I can also test that!
This was already pointed out in this archived post: https://itch.io/t/1158456/html5-local-storage-seems-to-be-shared-between-multipl...
Of course this is an annoying issue, especially if the local storage is shared between every author