You’re not alone in that problem. Ever since my iPhone se updated to iOS 13.1.2 my Touch ID stopped working altogether, Apple tech support had me do everything to it to try and fix it; still not working. They had me just reset it to factory settings and use it as a brand new device; Touch ID will work at set up but will still stop working after the set up. I’ve tried multiple times to set it up as a brand new device hoping that the Touch ID will work but it’s always the same outcome. I’ve given up already, I’ve just resorted to using pins to unlock my phone. I’ve disabled auto update on my iPad Pro. This is probably just another scheme from Apple to get the old iPhone users to buy the new ones or to make more money by trying to convince old iPhone users to have them fixed by “Apple Geniuses.”