I’d first check if the fingerprint sensor or the scan hole are dirty, and clean them. Afterwards, try erasing all the fingerprints and re-adding them. It’s possible that a software update started to pair displays to the motherboard, so one way of fixing this would be using a custom ROM. Hope this helps.
The Mi 9 SE is significantly smaller than the “standard” Mi 9. The display for one won’t fit the other, however, the guide applies to both devices, as it’s basically the usual way of display replacement. Good luck with your repair!