Actually there are plugins for VSCode, which allow to store data in the cloud and synchronize: Sync Settings
When downloading the settings according to the instructions, you need to enter the first Github token, and then Gist ID (although I checked, public gist's can still be viewed, but they do not appear in the profile to all but owner profile).
So, what to do if forgot token? On the page of the token it is possible to re-create:
But if the Sync Settings to enter the new token, and then Gist ID, the settings will pickup from gist'or not?