Chosen Solution
I had to replace the home button flex cable that runs along the LCD shield plate due to damage from a broken screen. Home button works, but touch ID does not. Original button assembly. Only parts swapped were the LCD, home button flex and shield plate, and then the flex cable with the front camera and proximity sensor. Any ideas on what to check? Reseated all of the connections a few times as well as resets and restores of the phone with no results. The flex cable was purchased elsewhere and not here.
I would look for any damage to the home button flex, under a microscope if available. I would also try a different flex cable that runs along the shield, just in case there is a fault in the one you got. Otherwise, it looks like you have done most other steps, rechecking the connections, and resetting the phone.
Normally rebooting the phone will fix this. Hold power and home until the apple appears, then release. If that doesn’t fix it, its more than likely damage to the flex cable attached to the home button, which I haven’t found a way to fix.