Chosen Solution
Iphone 8 home button only responding when on lock screen. Able to use touch ID to unlock phone. Once phone is unlocked phone does not respond when home button is pressed. Phone has most recent IOS 14.6software update. Attempted to calibrate home button based on Apple forums. Strange that the home button only responds to touch on lock screen and no where else. No notification that the phone is unable to activate touch ID. Also had the same thing occur on an Iphone 7 Plus; both up to date software and occurred this week.
It sounds like your home button is damaged. I suspect the reason that it appears to function on the lock screen is because the Touch ID sensor is actually doing the work, not the home button itself, then once the phone is open there is nothing more for the Touch ID sensor to do and the failed home button does nothing. I’ve seen this happen before when the home button is not treated delicately during a screen replacement. Because the home button is specific to the board the only way to restore functionality would be to bring it to Apple to have them replace it, or purchase and install an aftermarket home button that can connect to your phone via bluetooth (if I recall correctly). Hope this helps!