In theory you should be able to get Touch ID back with the original home button. Start out by trying a force restart and see if that brings it back.
[guide|133212|How to Force Restart the iPhone SE 2020 - iFixit Repair Guide|new_window=true]
If that doesn't do the trick, I'd suggest backing up the phone and doing a DFU update; that's the most complete update possible and will put your phone back to its original factory settings.
[link|https://www.macrumors.com/how-to/force-restart-iphone-se/|iPhone SE: How to Hard Reset or Enter DFU Mode - MacRumors|new_window=true]
If that still doesn't work I'm out of ideas, but hopefully if it comes to that there are lots of very smart people on here who will have more suggestions.