Let's say I have a personal and work account on a website and use them strictly on separate devices and ISP. If I have connected 2FA for both accounts to a single 2FA app's account, say Authy for example, does the website have any chances of finding that both the accounts are connected to me, explicitly through the 2FA app?
The website is completely unaware of the fact you are generating the 2FA with Authy or anything about the device that generated the 2FA code.
To make the scenario even more clear, imagine using single Authy account installed in my android, and that is connected to two Twitter accounts. Can Twitter find out both the twitter accounts are linked to one person, just because both gets 2FA codes from same Authy account from my android?
If you have two authenticators, tied to the same Authy account, then they are completely separate from one another. The website is completely and totally unaware you are actually using Authy to handle the codes. You can even install Authy on as many devices as you want.
I believe you are mistaking the terms authenticators and accounts, when it comes to 2FA, which was the cause of confusion.
Nope; That absolutely is false. Any website that offers 2FA authentication is unable to detect how you generate the 2FA code use to authenticate your account. I wasn’t actually confused.
Additionally, your opening statement assumed if I had two authenticators while I was pretty clear in my question that it involved a "single 2FA app's account". Which is why I went ahead with a clarifying comment.
Except you actually have two separate authenticators, they are just linked, to the same Authy account. I have 20 different Google Authenticators, synchronized across (Google Authenticators, Microsoft Authenticators, Last Pass, and Authy) on multiple devices.
My assumption is that each [website name here] account, would have their own Google Authenticator, linked to the same Authy account. You can replace “Google Authenticator” with any 2FA authenticator that the website (and Authy) in question supports.