Second time this has happened to me with my 7 Plus: all physical buttons stop working. I can't turn the screen off, I can't return to home, I can't change the volume, I can't multitask. The app I'm in in this case still works, I can scroll and type and it's fully functional. I just can't change apps or turn the phone screen off at all. Last time I solved it with a hard reset, this time I decided to wait it out. I let the screen turn off naturally, the home button let the screen come back on and unlock, but it wouldn't progress beyond the lock screen. I used the control center to launch Overcast (it was the last thing I was playing through audio), and suddenly all my button pressed happened at once. Home presses, multitasking, volume switches, all came through on a multi-minute delay
It's working fine now. Clearly software related since it queued up all my actions, still weird