if I buy a new Trezor and restore it using a seed-phrase, will the function allowing it to be used as a key for two-factor authentication also be restored?
Yes. The private keys used in the 2FA app are derived from the seed phrase, and so recovering the seed phrase will recover the 2FA app just as it would recover a bitcoin wallet.
You can see the relevant info on the Trezor wiki here:
Restoring a seed on another Trezor (see Recovery) restores all the U2F keys too, since they are derived from one master key. Due to the design of U2F, some services might implement a counter that records the number of sign-ins. However, if you have firmware version 1.4.2 or higher, the U2F counter is restored automatically.