how to use 2fa authentication with several facebook accounts?

i have a personal account that is setup to "Google Authenticator" - i have about 3-4 more accounts which i use with dedicated proxies on different browser profiles, some of them are asking me to either validate via SS and ID or a 3rd party 2fa authenticator tool (ex: Google Authenticator).

After researching it saying facebook will also accept Authy as an Authenticator?, is this going to leave footprints from my iphone if i use the Google Authenticator from my personal iPhone? or if i use another app like Authy for my other fake accounts?

I would just like to know if facebook grabs any data from my iPhone to see if i logged into anywhere else(ex cookies etc..)

Did you find any solution?

using it https://chrome.google.com/webstore/detail/authenticator/bhghoamapcdpbohphigoooaddinpkbai?hl=vi