There are many 2FA implementations out there, and surely some of them might actually tie to the hardware of the device you use.
The 2FA algorithm used here on this site does not
It's called TOTP (Time-based One Time Password)
and the input data to generate the current code is nothing but:
A) the secret key, which is included in that QR code you are supposed to scan but also is shown in plain text below it
B) the current time
There is no tracking possible on what device you generated a code.
If an authenticator app that you want to use for 2FA on here requests any more info from you or to sign into something or other BS, I recommend you to dump it and use a different one. The app doesn't need anything but the secret key in order to be able to generate codes for you.
I personally use FreeOTP, which is developed by a large company called Red Hat, but still open source
. You can get it for Android
. This app definitely does not ask any more info from you than it actually needs to work.