On TOTP-based 2FA (Time Based One Time Password), you have the seed, and the timestamp. At every interval (generally 30 seconds), the 2FA program concatenates the key and the timestamp, hashes it, cuts to a predefined size, and gives you the result.
To log in using TOTP, you will send this result to the server, and the server will do the same: concatenate the seed from your user (he has it stored) with the timestamp, hash, cut, and compare the result with the value you send. If it matches, good, access allowed.
You don't link 2FA accounts in any way. If you use Google Auth for a couple accounts, all you have done is to store the seed and the provider name (that you can edit freely) on a convenient application. You could even save the key to a text file and do the calculations by hand.
The problem is not linking the accounts, but leaking the database. Authy asks (requires?) a password for creating a backup database, so the copy you sent to their servers is an encrypted binary blob, and I don't think Authy stores the database password.
In case someone gets your phone (law enforcement, spouse, colleague) and opens the 2FA application, it can see all account labels and infer what kind of services you use. Using non descriptive labels (like calling GMail or Funny Cats the 2FA token for a sensitive service) can help keeping this list more private.