Apple has since released iOS 14.2.1 which is currently only available for the iPhone 12 series, and part of the changes that is part of the update is addressing touchscreen issues with the iPhone 12 mini. According to the changelog, it reads, “Lock Screen could become unresponsive on iPhone 12 mini.”
The update is being pushed out at this time of writing so you should be able to download it already. It’s interesting how this was a software issue as some had speculated that it might be a hardware one, where some have offered up theories that there might be some kind of grounding issue where the touchscreen would work if they touched the case while touching the screen, it would work.
Others have offered up other theories like how the case or screen protector acts as an insulation for the phone, thus rendering the capacitive display unresponsive in the process. In any case, hopefully this update will address those issues so be sure to download it if you’re one of those affected by it.