I have same problem on SE updated to iOS 13 on Friday, which had worked fine up until after the update.
Locked screen showed unlock key pad when placed close to Point of Sale (POS) device, then went to normal Home Screen when unlocked. Never went to Apple Pay screen.
Called Apple Support. After testing online, determined NFC chip functioning correctly.
Found Settings>Touch ID & Passcode>"Allow Access When Closed" defaulted to OFF. Reset to ON.
Unfortunately, cannot test until I access a POS device later in week.
Have similar problem with 6 and 6 Plus when updated to 12.4 in last few months. Thought old phones were dying. Apple Support tested both phones online, determined NFC chip functioning correctly. Will continue trying to recover those with resets and possible 8 hour round trip to Apple Store.