Sandboxing is a concept. It means running a game in an environment, where it does not have access to critical things. Games that run in a browser are sandboxed. Games that run on Android are mostly sandboxed. Games that run on an admin privileged windows user account are the opposite of sandboxed.
You asked for authenticators, so I assumed you are interested in security. Trying out new and indie games exposes you to amateur level developers and if you are unlucky, to malware. It is of course mostly a Windows problem that exists for decades. Any malicous programm could read the cookies of your browser. And any badly programmed app could mess with your system settings, or leave clutter at places where no clutter is supposed to be.
The sandbox method the itch app uses is to create a new user that has not the right to read the files of your main account. The game when started by the itch app runs as that user and only can mess with the files of that user.
If you use 2fa, print out the scratch codes. They are needed to restore your account, if you lose your phone with the 2fa app.
Regarding dangers on itch, you might be interested in
https://itch.io/t/1659440/psa-beware-the-try-my-game-scam
quote from the itch creator: "On itch.io, it is safe to view the page, but do not download any untrusted software" "Treat any page you encounter with suspicion if you are unable to vet the creators in any way."
This goes for pages encountered in recent or by random browsing as well. Scammers spam their malware and not all gets cought in time before some unsuspecting user finds the page. Some of the games in your collections went missing, because they were malware - if you are the type of user that puts games in collections to view later. Others are missing because the developer deleted it, or other reasons.