Why does my phone sometimes unlock with TouchID, but not go to home screen/app?
Are you using raise to wake? There is a timing that is difficult to duplicate, but can be repeated, where you can press the home button and raise to wake at the same time. The Touch ID unlocks the phone, but the wake seems to register from the raise instead of the home button press and so you stay on the lock screen instead of opening to the last app/home screen.

If you want the behavior of the phone being unlocked, but staying on the lock screen so you can look at your notifications, then just raise to wake, rest your finger on the home button, but don’t press until you’re ready to leave the lock screen.