For the 13 Series, the Face ID tiny authentication chip is in the feed-through cable between the motherboard and the panel, coded.
In the case of used iPhones that have undergone more serious servicing, Face ID has often stopped working, but in the case of the 13 series, the situation has become even more complicated, as the display of the mobiles is individually coded to the motherboard, the rice grain-sized processor and an authentication chip is soldered to the ribbon cable between the two components.
Of course, the solution is available to authorized Apple service centers and service partners contracted with the manufacturer who have direct access to the factory part, with which the units can be programmed, but at first there will certainly be few smaller services where this can be remedied.
Smaller repair companies will have the option of soldering the old chip off the cable and relocating the new one, but this is not a risk-free operation and due to the many small connectors you have to work very precisely, it seems almost impossible with a manual soldering iron. A very similar thing happened last year with the iPhone 12 series camera, in this regard we also wrote an article then involving one of the key players in the domestic repair industry, but in the meantime, Apple has backed out of the complete limitation of the unencrypted camera module, and after an iOS update, these cameras were working, only throwing an error message at startup.