Having the same problem since i bout my iPhone 12 Pro max day one. Not sure if its an iOS bug or its a hardware issue. Well we can say the hardware and the OS aren’t optimized but thats took too long to be fixed which make me feel thats its just a stutter gate. Im really really frustrated whenever i swipe home it’s randomly stutter like an old cheap phone. Im on 14.4.2 (18D70). I started to feel that apple cant and wont do anything about it, I hope I'm wrong but this is what its seems like so far. I hate it whenever i gi back to my iPhone XS Max i feel like its newer, faster and better in every way. Not to mention force touch 😒. I really regret upgrading from my XS max to the 12PM. 😣

Turn off VPN < happened to me when trying while VPN connected preventing the updated turn off all apps take off your smart battery case connect your phone directly to the charger that came with the iPhone in the box turn off audio playing in background Make sure its a fresh download if you reinstalled a new profile make sure to delete the update from storage in Settings then try agin restart your phone and try agin it should work if not after a few try, try updating using a computer