Hi Jonathan,
The screen itself isn't part of the Face ID system, but the earpiece speaker assembly mounted on it is, so if you follow the instructions in the guide and transfer the earpiece speaker assembly over to the new screen, then your Face ID should work fine.
[guide|140482|iPhone 12 mini Screen Replacement - iFixit Repair Guide|new_window=true]
The other main consideration in swapping screens is that you will need to copy the screen data over from the old screen to the new one in order to keep the True Tone function working. There are several programmers on the market that will do the trick such as the Qian Li iCopy device.
Finally, Apple has been making parts replacement harder by tying parts to the logic board using a proprietary encryption algorithm that can't be copied. The result is unless you use the Apple self repair program and buy the screen from them, you'll get a warning that pops up for the first week or so warning you that the screen might not be genuine - even if it is a genuine Apple screen. Outside of the Apple repair program, the only way to get rid of that warning is to desolder a chip from the old screen and move it to the new one. That's a repair that's beyond the capability of most of us home DIY-ers, as it requires somewhat specialized equipment and expertise. The obvious choice for most of us is to ignore the warning for the time it pops up, and after that it will only show up in the settings.